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Call number: | 9780813345475:ONLINE Show nearby items on shelf |
Title: | A First Course In Chaotic Dynamical Systems [electronic resource] Theory And Experiment |
Author(s): |
Robert L. Devaney |
Publisher: | Addison-Wesley |
Size: | 1 electronic resource (302 pages) p |
Contents: | A mathematical and historical tour -- Examples of dynamical systems -- Orbits -- Graphical analysis -- Fixed and periodic points -- Bifurctions -- The quadratic family -- Transition to chaos -- Symbolic dynamics -- Chaos -- Sarkovskii's theorem -- T he role of the critical orbit -- Newton's method -- Fractals -- Complex functions -- The Julia set -- The Madelbrot set -- Further projects and experiments. |
ISBN: | 9780813345475 |
Keywords: | Chaotic behavior in systems , Differentiable dynamical systems |
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Call number: | 9780511809187:ONLINE Show nearby items on shelf |
Title: | Introduction to the modern theory of dynamical systems [electronic resource] |
Author(s): |
Anatole Katok Boris Hasselblatt |
Date: | 1995 |
Publisher: | New York: Cambridge University Press |
Size: | 1 online resource (802 p.) |
Note: | unlimited access |
Contents: | pt. 1. Examples and fundamental concepts. 1. First examples. 1. Maps with stable asymptotic behavior. 2. Linear maps. 3. Rotations of the circle. 4. Translations on the torus. 5. Linear flow on the torus and completely integrable systems. 6. Gradien t flows. 7. Expanding maps. 8. Hyperbolic toral automorphisms. 9. Symbolic dynamical systems. 2. Equivalence, classification, and invariants. 1. Smooth conjugacy and moduli for maps. 2. Smooth conjugacy and time change for flows. 3. Topological conjugacy, factors, and structural stability. 4. Topological classification of expanding maps on a circle. 5. Coding, horseshoes, and Markov partitions. 6. Stability of hyperbolic toral automorphisms. 7. The fast-converging iteration method (Newton method) for the conjugacy problem. 8. The Poincare-Siegel Theorem. 9. Cocycles and cohomological equations. 3. Principal classes of asymptotic topological invariants. 1. Growth of orbits. 2. Examples of calculation of topological entropy. |
ISBN: | 9780521341875 |
Series: | eBooks |
Series: | Cambridge Books Online |
Keywords: | Differentiable dynamical systems. |
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Call number: | SPRINGER-2014-9788847055049:ONLINE Show nearby items on shelf |
Title: | Modelli Dinamici Discreti [electronic resource] |
Author(s): |
Ernesto Salinelli Franco Tomarelli |
Date: | 2014 |
Edition: | 3a edizione |
Publisher: | Milano : Springer Milan : Imprint: Springer |
Size: | 1 online resource |
Note: | Questo volume fornisce una introduzione allanalisi dei sistemi dinamici discreti. La materia presentata mediante un approccio unitario tra il punto di vista modellistico e quello di varie discipline che sviluppano metodi dianalisi e tecniche risolut ive: Analisi Matematica, Algebra Lineare, Analisi Numerica, Teoria dei Sistemi, Calcolo delle Probabilit. Allesame di unampia serie di esempi, segue la presentazione degli strumenti per lo studio disistemi dinamici scalari lineari e non lineari, con parti colare attenzione allanalisi della stabilit. Si studiano in dettaglio le equazioni alle differenze lineari e si fornisce una introduzione elementare alle trasformate Z eDFT. Un capitolo dedicato allo studio di biforcazioni e dinamiche caotiche. I sistemi dinamici vettoriali ad un passo e le applicazioni alle catene di Markov sono oggetto di tre capitoli. Lesposizione autocontenuta: leappendici tematiche presentano prerequisiti, algoritmi e suggerimenti per simulazioni al computer. Ai numerosi esempi pro posti si affianca un gran numero di esercizi, per la maggior parte dei quali si fornisce una soluzionedettagliata. Il volume indirizzato principalmente agli studenti di Ingegneria, Scienze, Biologia ed Economia. Questa terza edizione comprende laggiornam ento di vari argomenti, laggiunta di nuovi esercizi e lampliamentodella trattazione relativa alle matrici positive ed alle loro propriet utili nellanalisi di sistemi, reti e motori di ricerca |
Contents: | 1 Fenomeni ricorsivi ed equazioni alle differenze |
2 Equazioni alle differenze lineari | |
3 Sistemi dinamici discreti: equazioni scalari ad un passo | |
4 Complessit dei sistemi dinamici non lineari: biforcazioni e caos | |
5 Sistemi dinamici discreti: equazioni vettoriali | |
6 Catene di Markov | |
7 Matrici positive e grafi | |
8 Soluzioni degli esercizi | |
Appendice A | |
Somme e serie | |
Appendice B | |
Numeri Complessi | |
Appendice C | |
Aritmetica della probabilit | |
Appendice D | |
Algebra lineare | |
Appendice E | |
Topologia | |
Appendice F | |
Dimensione frattale | |
Appendice G | |
Tabelle di Z | |
tra | |
ISBN: | 9788847055049 |
Series: | eBooks |
Series: | SpringerLink |
Series: | UNITEXT, 2038-5714 : v71 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Functional equations , Differentiable dynamical systems |
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Call number: | SPRINGER-2014-9784431551089:ONLINE Show nearby items on shelf |
Title: | Weakly Wandering Sequences in Ergodic Theory [electronic resource] |
Author(s): |
Stanley Eigen Arshag Hajian Yuji Ito Vidhu Prasad |
Date: | 2014 |
Publisher: | Tokyo : Springer Japan : Imprint: Springer |
Size: | 1 online resource |
Note: | The appearance of weakly wandering (ww) sets and sequences for ergodic transformations over half a century ago was an unexpected and surprising event. In time it was shown that ww and related sequences reflected significant anddeep properties of ergo dic transformations that preserve an infinite measure. This monograph studies in a systematic way the role of ww and related sequences in the classification of ergodic transformations preserving an infinitemeasure. Connections of these sequences to additi ve number theory and tilings of the integers are also discussed. The material presented is self-contained and accessible to graduate students. A basic knowledge of measure theory isadequate for the reader |
ISBN: | 9784431551089 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Functional analysis , Number theory |
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Call number: | SPRINGER-2014-9783662441404:ONLINE Show nearby items on shelf |
Title: | Theory and Applications of Difference Equations and Discrete Dynamical Systems [electronic resource] : ICDEA, Muscat, Oman, May 26 - 30, 2013 |
Author(s): |
Ziyad AlSharawi Jim M Cushing Saber Elaydi |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This volume contains the proceedings of the 19th International Conference on Difference Equations and Applications, held at Sultan Qaboos University, Muscat, Oman in May 2013. The conference brought together experts and novices inthe theory and appli cations of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete time dynamical systems with applications to mathematical sciences and, in particular,mathematical biology, ecology, and epidemi ology. It includes four invited papers and eight contributed papers. Topics covered include: competitive exclusion through discrete time models, Benford solutions of linear differenceequations, chaos and wild chaos in Lorenz-type systems, advances in peri odic difference equations, the periodic decomposition problem, dynamic selection systems and replicator equations, and asymptotic equivalence of differenceequations in Banach Space. This book will appeal to researchers, scientists, and educators who work in the fields of difference equations, discrete time dynamical systems and their applications. |
Contents: | Papers by Invited Speakers: Competitive exclusion through discrete time models: Azmy S. Ackleh and Paul L. Salceanu |
Benford solutions of linear difference equations: Arno Berger and Gideon Eshun | |
Harvesting and dynamics in some one | |
dimensional population models: Eduardo Liz and Frank M. Hilker | |
Chaos and wild chaos in Lorenz | |
type systems: Hinke M. Osinga, Bernd Krauskopf and Stefanie Hittmeyer | |
Contributed Papers: Almost automorphic sequences and their application to a model of cellular neural network: Syed Abbas | |
Advances in periodic difference equations with open problems: Ziyad A | |
ISBN: | 9783662441404 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v102 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional equations , Differentiable dynamical systems , Genetics Mathematics |
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Call number: | SPRINGER-2014-9783662439203:ONLINE Show nearby items on shelf |
Title: | Geometry and Analysis of Fractals [electronic resource] : Hong Kong, December 2012 |
Author(s): |
De-Jun Feng Ka-Sing Lau |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written bythe leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong.The volume offers insights into a number o f exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematicalphysics. |
Contents: | Mandelbrot cascades and related topics |
Law of pure types and some exotic spectra of fractal spectral measures | |
The role of transfer operators and shifts in the study of fractals: encoding | |
models, analysis and geometry, commutative and non | |
commutative | |
Generalized energy inequalities and higher multifractal moments | |
Some Aspects of Multifractal analysis | |
Heat kernels on metric measure spaces | |
Stochastic completeness of jump processes on metric measure spaces | |
Self similar sets, entropy and additive combinatorics | |
Quasisymmetric modification of metrics on self | |
similar sets | |
Re | |
ISBN: | 9783662439203 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v88 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783642545931:ONLINE Show nearby items on shelf |
Title: | Neural Fields [electronic resource] : Theory and Applications |
Author(s): |
Stephen Coombes Peter beim Graben Roland Potthast James Wright |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | With this book, the editors present the first comprehensive collection in neural field studies, authored by leading scientists in the field - among them are two of the founding-fathers of neural field theory. Up to now, researchresults in the field h ave been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. Starting with a tutorial for novices in neural field studies, thebook comprises chapters on emergent pattern s, their phase transitions and evolution, on stochastic approaches, cortical development, cognition, robotics and computation, large-scale numerical simulations, the coupling of neural fieldsto the electroencephalogram and phase transitions in anesthesia. The intended readership are students and scientists in applied mathematics, theoretical physics, theoretical biology, and computational neuroscience. Neural field theoryand its applications have a long-standing tradition in the mathematical and computati onal neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan,Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Bressloff, Haken, and Wright. Since then, much progress has been made in both, the development of mathematical andnumerical techniques, and in physiological refinement and understanding. In contrast to large-scale neural network models desc ribed by huge connectivity matrices that are computationally expensive in numerical simulations, neural fieldmodels described by connectivity kernels allow for analytical treatment by means of functional analysis methods. Thus, a number of rigorous result s on the existence of bump and wave solutions or on inverse kernel construction problemsare nowadays available. Moreover, neural fields provide an important interface for the coupling of continuous neur |
Contents: | Preface |
1.Tutorial on Neural Field Theory. S. Coombes, P. beim Graben and R. Potthast | |
Part I Theory of Neural Fields | |
2.A Personal Account of the Development of the Field Theory of Large | |
Scale Brain Activity from 1945 Onward. J. Cowan | |
3.HeavisideWorld: Excitation and Self | |
Organization of Neural Fields. Shun | |
ichi Amari | |
4.Spatiotemporal Pattern Formation in Neural Fields with Linear Adaptation. G.B. Ermentrout, S.E. Folias and Z.P. Kilpatrick | |
5.PDE Methods for Two | |
Dimensional Neural Fields. C.R. Laing | |
6.Numerical Simulation Scheme of One | |
and Two Dimensional Neural Fields Inv | |
ISBN: | 9783642545931 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Functional analysis , Integral equations , Consciousness |
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Call number: | SPRINGER-2014-9783642405235:ONLINE Show nearby items on shelf |
Title: | An Introduction to Markov Processes [electronic resource] |
Author(s): |
Daniel W Stroock |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including studentsfrom engineering, econ omics, physics, and biology. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time processes.Applications are dispersed throughout the book. In addition, a whole chapter isdevoted to reversible processes and the use of thei r associated Dirichlet forms to estimate the rate of convergence to equilibrium. These results are then applied to the analysis of the Metropolis (a.k.a simulated annealing) algorithm.The corrected and enlarged 2nd edition contains a new chapter in which the author develops computational methods for Markov chains on a finite state space. Most intriguing isthe section with a new technique for computing stationarymeasures, which is applied to derivations of Wilson's algorithm and Kirchoff's formula for span ning trees in a connected graph |
Contents: | Preface |
Random Walks, a Good Place to Begin | |
Doeblin's Theory for Markov Chains | |
Stationary Probabilities | |
More about the Ergodic Theory of Markov Chains | |
Markov Processes in Continuous Time | |
Reversible Markov Processes | |
A minimal Introduction to Measure Theory | |
Notation | |
References | |
Index | |
ISBN: | 9783642405235 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Graduate Texts in Mathematics, 0072-5285 : v230 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319082516:ONLINE Show nearby items on shelf |
Title: | Recent Advances in Delay Differential and Difference Equations [electronic resource] |
Author(s): |
Ferenc Hartung Mihly Pituk |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering, and control theory. In this volume, the participants of the International Conference on Delay Differential andDifference Equations and Applications, Balatonfred, Hungary, July 15-19, 2013 present recent research in this quickly-evolving field. The papers relate to the existence, asymptotic, and oscillatory properties of the solutions |
Contents: | On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity |
Comparison Theorems for Second Order Functional Differential Equations | |
Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems using Transformations | |
Almost Oscillatory Solutions of Second Order Difference Equations of Neutral Type | |
Uniform Weak Disconjugacy and Principal Solutions for Linear Hamiltonian Systems | |
Stability Criteria for Delay Differential Equations | |
Anal | |
ISBN: | 9783319082516 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v94 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional equations , Differentiable dynamical systems |
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Call number: | SPRINGER-2014-9783319082288:ONLINE Show nearby items on shelf |
Title: | Dynamical Systems Generated by Linear Maps [electronic resource] |
Author(s): |
emal B Dolianin Anatolij B Antonevich |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The book deals with dynamical systems, generated by linear mappings of finite dimensional spaces and their applications. These systems have a relatively simple structure from the point of view of the modern dynamical systemstheory. However, for the d ynamical systems of this sort, it is possible to obtain explicit answers to specific questions being useful in applications. The considered problems are natural and look rather simple, but in reality in thecourse of investigation, they confront users with plenty of subtle questions, and their detailed analysis needs a substantial effort. The problems arising are related to linear algebra and dynamical systems theory, and therefore, thebook can be considered as a natural amplification, refinement and supple ment to linear algebra and dynamical systems theory textbooks |
Contents: | From the Contents: Introduction |
Vector trajectory | |
The Jordan basis and special subspaces | |
Representation of the vector trajectory | |
The structures related to the principal term of the vector Trajectory | |
The asymptotic behavior of vector trajectories and trajectories of one | |
dimensional subspaces | |
ISBN: | 9783319082288 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Engineering , Vibration |
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Call number: | SPRINGER-2014-9783319068206:ONLINE Show nearby items on shelf |
Title: | Dynamical Systems with Applications using MATLAB [electronic resource] |
Author(s): |
Stephen Lynch |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applicationsand simulation utilizi ng MATLAB, Simulink, the Image Processing Toolbox, and the Symbolic Math Toolbox, including MuPAD. Features new to the second edition include sections on series solutions ofordinary differential equations, perturbation methods, normal forms, Grbner bas es, and chaos synchronization chapters on image processing and binary oscillator computing hundreds of newillustrations, examples, and exercises with solutions and over eighty up-to-date MATLAB program files and Simulink model files available online. T hese files were voted MATLAB Central Pick of the Week in July2013. The hands-on approach of Dynamical Systems with Applications using MATLAB, Second Edition, has minimal prerequisites, only requiring familiarity with ordinary differential equations. It w ill appeal to advanced undergraduateand graduate students, applied mathematicians, engineers, and researchers in a broad range of disciplines such as population dynamics, biology, chemistry, computing, economics, nonlinear optics, neural networks, and phy sics. Praise for the first edition Summing up, it can be said that this text allows the reader to have an easy and quick start to the huge field of dynamicalsystems theory. MATLAB/SIMULINK facilitate this approach under the aspect of learning by doing. OR News/Operations Research Spectrum The MATLAB programs are kept as simple as possible and the author's experience has shown thatthis method of teaching using MATLAB works well with computer laboratory classes of small sizes. I recommend Dynamical Syst ems with App |
Contents: | Preface |
A Tutorial Introduction to MATLAB | |
Linear Discrete Dynamical Systems | |
Nonlinear Discrete Dynamical Systems | |
Complex Iterative Maps | |
Electromagnetic Waves and Optical Resonators | |
Fractals and Multifractals | |
The Image Processing Toolbox | |
Differential Equations | |
Planar Systems | |
Interacting Species | |
Limit Cycles | |
Hamiltonian Systems, Lyapunov Functions, and Stability | |
Bifurcation Theory | |
Three | |
Dimensional Autonomous Systems and Chaos | |
Poincar Maps and Nonautonomous Systems in the Plane | |
Local and Global Bifurcations | |
The Second Part of Hilbert's Sixte | |
ISBN: | 9783319068206 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Differential Equations , Engineering mathematics |
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Call number: | SPRINGER-2014-9783319063430:ONLINE Show nearby items on shelf |
Title: | Nonlinear Dynamics and Quantum Chaos [electronic resource] : An Introduction |
Author(s): |
Sandro Wimberger |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlineardynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems'theory combining in a comprehensive way cla ssical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases theunderstanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well asfor researchers starting to work in the field |
Contents: | Introduction |
Fundamental terminology | |
Complexity | |
Classical versus quantum dynamics | |
Problems | |
References | |
Dynamical systems | |
Evolution law | |
One | |
dimensional maps | |
Problems | |
References | |
Nonlinear Hamiltonian systems | |
Integrable examples | |
Hamiltonian formalism | |
Important techniques in the Hamiltonian formalism | |
Integrable systems | |
Non | |
integrable systems | |
Perturbation of low | |
dimensional systems | |
Canonical perturbation theory | |
Transition to chaos in Hamiltonian systems | |
Criteria for local and global chaos | |
Appendix | |
Problems | |
References | |
Aspects | |
ISBN: | 9783319063430 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Graduate Texts in Physics, 1868-4513 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Differentiable dynamical systems , Mathematical physics , Mechanics |
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Call number: | SPRINGER-2014-9783319057231:ONLINE Show nearby items on shelf |
Title: | Invariant Probabilities of Transition Functions [electronic resource] |
Author(s): |
Radu Zaharopol |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transitionfunctions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated usingtransition functions defined by flows, semiflows, a nd one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 areextended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structureof the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of the state space, where the invariant ergodic probability measures play a significant role. Other topics covered include: characterizationsof the supports of various types of invariant probability measures and the use of these to obtain criteria for un ique ergodicity, and the proofs of two mean ergodic theorems for a certain type of transition functions. The book will beof interest to mathematicians working in ergodic theory, dynamical systems, or the theory of Markov processes. Biologists, physicists and economists interested in interacting particle systems and rigorous mathematics will also findthis book a valuable resource. Parts of it are suitable for advanced graduate courses. Prerequisites are basic notions and results on functional analysis, gen eral topology, measure theory, the Bochner integral and some of itsapplications |
Contents: | Introduction |
1.Transition Probabilities | |
2.Transition Functions | |
3.Vector Integrals and A.E. Convergence | |
4.Special Topics | |
5.The KBBY Ergodic Decomposition, Part I | |
6.The KBBY Ergodic Decomposition, Part II | |
7.Feller Transition Functions | |
Appendices: A.Semiflows and Flows: Introduction | |
B.Measures and Convolutions | |
Bibliography | |
Index | |
ISBN: | 9783319057231 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Probability and Its Applications, 1431-7028 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Operator theory , Potential theory (Mathematics) , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319048079:ONLINE Show nearby items on shelf |
Title: | Analytic and Probabilistic Approaches to Dynamics in Negative Curvature [electronic resource] |
Author(s): |
Franoise Dal'Bo Marc Peign Andrea Sambusetti |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The work of E. Hopf and G.A. Hedlund, in the 1930s, on transitivity and ergodicity of the geodesic flow for hyperbolic surfaces, marked the beginning of the investigation of the statistical properties and stochastic behavior ofthe flow. The first cen tral limit theorem for the geodesic flow was proved in the 1960s by Y. Sinai for compact hyperbolic manifolds. Since then, strong relationships have been found between the fields of ergodic theory, analysis, andgeometry. Different approaches and new tools have been developed to study the geodesic flow, including measure theory, thermodynamic formalism, transfer operators, Laplace operators, and Brownian motion. All these different points ofview have led to a deep understanding of more general dynamical sy stems, in particular the so-called Anosov systems, with applications to geometric problems such as counting, equirepartition, mixing, and recurrence properties of theorbits. This book comprises two independent texts that provide a self-contained introduct ion to two different approaches to the investigation of hyperbolic dynamics. The first text, by S. Le Borgne, explains the method of martingalesfor the central limit theorem. This approach can be used in several situations, even for weakly hyperbolic flow s, and the author presents a good number of examples and applications to equirepartition and mixing. The second text, by F.Faure and M. Tsujii, concerns the semiclassical approach, by operator theory: chaotic dynamics is described through the spectrum of the associated transfer operator, with applications to the asymptotic counting of periodic orbits. Thebook will be of interest for a broad audience, from PhD and Post-Doc students to experts working on geometry and dynamics |
ISBN: | 9783319048079 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer INdAM Series, 2281-518X : v9 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Operator theory , Global differential geometry , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319040752:ONLINE Show nearby items on shelf |
Title: | Twisted Teichmller Curves [electronic resource] |
Author(s): |
Christian Wei |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | These notes introduce a new class of algebraic curves on Hilbert modular surfaces. These curves are called twisted Teichmller curves, because their construction is very reminiscent of Hirzebruch-Zagier cycles. These new objectsare analyzed in detail and their main properties are described. In particular, the volume of twisted Teichmller curves is calculated and their components are partially classified. The study of algebraic curves on Hilbert modularsurfaces has been widely covered in the literature due to their arithmetic importance. Among these, twisted diagonals (Hirzebruch-Zagier cycles) are some of the most important examples |
Contents: | Introduction |
Background | |
Teichmller Curves | |
Twisted Teichmller Curves | |
Stabilizer and Maximality | |
Calculations for Twisted Teichmller Curves | |
Prym Varieties and Teichmller Curves | |
Lyapunov Exponents | |
Kobayashi Curves Revisited | |
Appendix | |
Tables | |
List of Symbols | |
Index | |
Bibliography | |
ISBN: | 9783319040752 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2104 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Differentiable dynamical systems , Number theory |
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Call number: | SPRINGER-2014-9783319022918:ONLINE Show nearby items on shelf |
Title: | Discrete Dynamical Models [electronic resource] |
Author(s): |
Ernesto Salinelli Franco Tomarelli |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several disciplineas Mathematical Analysi s, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems arepresented, paying particular attention to the stabil ity analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to thestudy of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. Thebook is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Eco nomics. The exposition is self-contained: some appendices present prerequisites, algorithms and suggestions for computer simulations.The analysis of several examples is enriched by the proposition of many related exercises of increasing difficulty in the last chapter the detailed solution is given for most of them |
Contents: | 1 Recursive phenomena and difference equations |
2 Linear difference equations | |
3 Discrete dynamical systems: one | |
step scalar equations | |
4 Complex behavior of nonlinear dynamical systems: bifurcations and chaos | |
5 Discrete dynamical systems: vector equations | |
6 Markov chains | |
7 Matrix | |
8 Solutions | |
ISBN: | 9783319022918 |
Series: | eBooks |
Series: | SpringerLink |
Series: | UNITEXT, 2038-5714 : v76 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Functional equations , Differentiable dynamical systems |
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Call number: | SPRINGER-2014-9781493904198:ONLINE Show nearby items on shelf |
Title: | Ergodic Theory, Open Dynamics, and Coherent Structures [electronic resource] |
Author(s): |
Wael Bahsoun Christopher Bose Gary Froyland |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This book is comprised of selected research articles developed from a workshop onErgodic Theory, Probabilistic Methods and Applications, held in April 2012 at the BanffInternational Research Station.It contains contributionsfrom world leading experts in ergodic theory, dynamical systems, numerical analysis, fluid dynamics, and networks.The volume will serve asa valuable reference for mathematicians, physicists, engineers, physical oceanographers,atmospheric scientists, biologists, and climate scientis ts, who currently use, or wish to learn how to use, probabilistic techniques to cope with dynamical models that display open, coherent, or non-equilibrium behavior |
Contents: | 1. Nonautonomous flows as open dynamical systems: characterising escape rates and time |
varying boundaries | |
2. Eigenvalues of transfer operators for dynamical systems with holes | |
3. Periodic points, escape rates and escape measures | |
4. A multi | |
time step method to compute optical flow with scientific priors for observations of a fluidic system | |
5. Numerical approximation of conditionally invariant measures via maximum entropy | |
6. Lebesgue ergodicity of a dissipative subtractive algorithm | |
7. Improved estimates of survival probabilities via isospectral transformations | |
8. Dispersing | |
ISBN: | 9781493904198 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v70 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Mathematical optimization , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9781493902927:ONLINE Show nearby items on shelf |
Title: | Advanced H Control [electronic resource] : Towards Nonsmooth Theory and Applications |
Author(s): |
Yury V Orlov Luis T Aguilar |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This compact monographis focused ondisturbance attenuation in nonsmooth dynamic systems, developing anH approach in the nonsmooth setting. Similar to the standard nonlinear H approach, the proposed nonsmooth designguarantees both the internal asympto tic stability of anominal closed-loop system and the dissipativity inequality, which statesthat the size of an error signal is uniformly bounded with respect to the worst-case size of an externaldisturbance signal. This guarantee is achieved by constructi ng an energy or storage function that satisfies the dissipativity inequality andis then utilized as a Lyapunov functiontoensurethe internal stability requirements. Advanced H Control is unique in the literature for its treatment of disturbance attenuation in nonsmooth systems. It synthesizes various tools, including HamiltonJacobiIsaacs partial differential inequalities as well asLinear Matrix Inequalities. Along with the finite-dimensional treatment, the synthesis is extended to infinite-dimensional sett ing, involving time-delay and distributed parameter systems. To help illustrate this synthesis, the bookfocuses onelectromechanical applicationswithnonsmooth phenomena caused by dry friction, backlash, and sampled-data measurements. Special attention is d evoted to implementation issues. Requiring familiarity with nonlinearsystems theory, this book will be accessible to graduate students interested in systems analysis and design, and is a welcome additionto the literature forresearchers and practitioners in these areas |
Contents: | Part I Introduction |
1 Linear H1 control of autonomous systems | |
2 LMI approach in infinite dimensional setting | |
3 Linear H1 control of time | |
varying systems | |
4 Nonlinear H1 control | |
Part II Nonsmooth H1 Control | |
5 Elements of nonsmooth analysis | |
6 Synthesis of nonsmooth systems | |
7 LMI | |
based H1 boundary control of nonsmooth parabolic and hyperbolic systems | |
Part III Benchmark Applications | |
8 Advanced H1 synthesis of fully actuated robot manipulators with frictional joints | |
9 Nonsmooth H1 synthesis in the presence of backlash | |
10 H1 generation of periodic motion | |
11 LMI | |
ISBN: | 9781493902927 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Systems & Control: Foundations & Applications, 2324-9749 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Differential equations, partial , Systems theory , Engineering mathematics , Vibration |
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Call number: | SPRINGER-2014-9781461491613:ONLINE Show nearby items on shelf |
Title: | Nonlinear Maps and their Applications [electronic resource] : Selected Contributions from the NOMA 2011 International Workshop |
Author(s): |
Clara Grcio Daniele Fournier-Prunaret Tetsushi Ueta Yoshifumi Nishio |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | In the field of Dynamical Systems, nonlinear iterative processes play an important role. Nonlinear mappings can be found as immediate models for many systems from different scientific areas, such as engineering, economics,biology, or can also be obta ined via numerical methods permitting to solve non-linear differential equations. In both cases, the understanding of specific dynamical behaviors and phenomena is of the greatest interest for scientists.This volume contains papers that were presented at the International Workshop on Nonlinear Maps and their Applications (NOMA 2011) held in vora, Portugal, on September 15-16, 2011. This kind of collaborative effort is of paramountimportance in promoting communication among the various groups that work in dynamical systems and networks in their research theoretical studies as well as for applications. This volume is suitable for graduate students as well asresearchers in the field |
Contents: | J. P. Almeida A. A. Pinto D. A. Rand, Renormalization of circlediffeomorphism sequences and Markov sequences |
F. Balibrea M. V. Caballero, Examples of Lyapunov exponents in two dimensional systems | |
R. A. da Costa S. N. Dorogovtsev A.V. Goltsev J. F. F. Mendes, Characteristics of the explosive percolation transition | |
E. S. Roberts A. Annibale A. C. C. Coolen, Controlled Markovian dynamics of graphs: unbiased generation of random graphs with prescribed topological properties | |
G. Bettencourt, A case leading to rationalist of the drift | |
L. S. Efremova, Remarks on the nonwanderi | |
ISBN: | 9781461491613 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v57 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems |
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Call number: | SPRINGER-2014-9781461490388:ONLINE Show nearby items on shelf |
Title: | Infinite-Horizon Optimal Control in the Discrete-Time Framework [electronic resource] |
Author(s): |
Jol Blot Nala Hayek |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | In this bookthe authors takea rigorous look at the infinite-horizon discrete-time optimalcontrol theory from the viewpoint of Pontryagins principles. Several Pontryagin principles are described which govern systems andvarious criteria which define th e notions of optimality, along with a detailed analysis of how each Pontryagin principle relate to each other. The Pontryagin principle is examined in a stochastic setting and results are given whichgeneralize Pontryagins principles to multi-criteria prob lems. Infinite-Horizon Optimal Control in the Discrete-Time Frameworkis aimed toward researchers and PhD students in various scientific fields such as mathematics,applied mathematics, economics, management, sustainable development (such as, of fisheries a nd of forests), and Bio-medical sciences who are drawn to infinite-horizon discrete-time optimal control problems |
Contents: | 1. Presentation of the problems and tools of the finite horizon |
2. Infinite horizon theorems | |
3. The special case of the bounded processes | |
Related topics. Appendix A : Sequences | |
Appendix B: Static optimization | |
References | |
ISBN: | 9781461490388 |
Series: | eBooks |
Series: | SpringerLink |
Series: | SpringerBriefs in Optimization, 2190-8354 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Functional analysis , Mathematical optimization |
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Call number: | SPRINGER-2014-9781461486152:ONLINE Show nearby items on shelf |
Title: | Constructive Nonsmooth Analysis and Related Topics [electronic resource] |
Author(s): |
Vladimir F Demyanov Panos M Pardalos Mikhail Batsyn |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This volume contains a collection of papers based on lectures and presentations delivered at the International Conference on Constructive Nonsmooth Analysis (CNSA) held in St. Petersburg (Russia) from June 18-23, 2012. Thisconference was organized to mark the 50th anniversary of the birth of nonsmooth analysis and nondifferentiable optimization and was dedicated to J.-J. Moreau and the late B.N. Pshenichnyi, A.M. Rubinov, and N.Z. Shor, whosecontributions to NSA and NDO remain invaluable. The first f our chapters of the book are devoted to the theory of nonsmooth analysis. Chapters 5-8 contain new results in nonsmooth mechanics and calculus of variations. Chapters 9-13 arerelated to nondifferentiable optimization, and the volume concludes with four ch apters containing interesting and important historical chapters, including tributes to three giants of nonsmooth analysis, convexity, and optimization:Alexandr Alexandrov, Leonid Kantorovich, and Alex Rubinov. The last chapter provides an overview and imp ortant snapshots of the 50-year history of convex analysis and optimization |
Contents: | Constructive Noonsmooth Analysis and Related Topics (V. Demyanov, P.M. Pardalos, M. Batsyn) |
Use Model Theory in Nonsmooth Analysis (S.S. Kutateladze) | |
Demyanov Difference in Infinite Dimensional Spaces (J. Grzybowski, D. Pallaschke, R. Urbanski) | |
Separable Reduction of Metric Regularity Properties (A.D. Ioffe) | |
Construction of Pairs of Reproducing Kernel Banach Spaces (P.G. Georgiev, L. Sanchez | |
Gonzalez, P.M. Pardalos) | |
On the Regularization Method in Nondifferentiable Optimization Applied to Hemivariational Inequalities (N. Ovcharova, J. Gwinner) | |
Dynamics and Optimization of Mul | |
ISBN: | 9781461486152 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Optimization and Its Applications, 1931-6828 : v87 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Algorithms , Computer science , Mathematical optimization |
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Call number: | SPRINGER-2014-9781447153610:ONLINE Show nearby items on shelf |
Title: | Probability Theory [electronic resource] : A Comprehensive Course |
Author(s): |
Achim Klenke |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineeringand computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms. To addressthese concepts, the title covers a wide variet y of topics, many of which are not usually found in introductory textbooks, such as: limit theorems for sums of random variables martingales percolation Markov chains andelectrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integral and stochasticdifferential equations. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts inprobability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulat ions and some difficult proofs have been made more accessible. A wealth ofexamples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathe matics and statistics in physics, computer science,economics and biology |
Contents: | Basic Measure Theory |
Independence | |
Generating Functions | |
The Integral | |
Moments and Laws of Large Numbers | |
Convergence Theorems | |
Lp | |
Spaces and the RadonNikodym Theorem | |
Conditional Expectations | |
Martingales | |
Optional Sampling Theorems | |
Martingale Convergence Theorems and Their Applications | |
Backwards Martingales and Exchangeability | |
Convergence of Measures | |
Probability Measures on Product Spaces | |
Characteristic Functions and the Central Limit Theorem | |
Infinitely Divisible Distributions | |
Markov Chains | |
Convergence of Markov Chains | |
Markov Chains and Electr | |
ISBN: | 9781447153610 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9789462390034:ONLINE Show nearby items on shelf |
Title: | Normally Hyperbolic Invariant Manifolds [electronic resource] : The Noncompact Case |
Author(s): |
Jaap Eldering |
Date: | 2013 |
Publisher: | Paris : Atlantis Press : Imprint: Atlantis Press |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph treats normally hyperbolic invariant manifolds, with a focus on noncompactness. These objects generalize hyperbolic fixed points and are ubiquitous in dynamical systems. First, normally hyperbolic invariantmanifolds and their relation to hyperbolic fixed points and center manifolds, as well as, overviews of history and methods of proofs are presented. Furthermore, issues (such as uniformity and bounded geometry) arising due tononcompactness are discussed in great detail with examples. The main new result shown is a proof of persistence for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. This extends well-knownresults by Fenichel and Hirsch, Pugh and Shub, and is complementary to noncompac tness results in Banach spaces by Bates, Lu and Zeng. Along the way, some new results in bounded geometry are obtained and a framework is developed toanalyze ODEs in a differential geometric context. Finally, the main result is extended to time and parame ter dependent systems and overflowing invariant manifolds |
Note: | Springer eBooks |
Contents: | Introduction |
Manifolds of bounded geometry | |
Persistence of noncompact NHIMs | |
Extension of results | |
ISBN: | 9789462390034 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Atlantis Series in Dynamical Systems : v2 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems |
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Call number: | SPRINGER-2013-9783642394850:ONLINE Show nearby items on shelf |
Title: | Algebras, Quivers and Representations [electronic resource] : The Abel Symposium 2011 |
Author(s): |
Aslak Bakke Buan Idun Reiten yvind Solberg |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book features survey and research papers from The Abel Symposium 2011, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas ofmathematics like commutati ve algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systemsand triangulated categories. In addition, it in cludes contributions on further developments in representation theory of quivers and algebras. Algebras, Quivers and Representations is targeted at researchers and graduate students inalgebra, representation theory and triangulated categories |
Note: | Springer eBooks |
Contents: | C. Amiot: Preprojective algebras, singularity categories and orthogonal decompositions |
L. Avramov: (Contravariant) Koszul duality for DG algebras | |
R. Buchweitz: The fundamental group of a morphism in a triangulated category | |
K. Erdmann: On Hochschild cohomology of weakly symmetric special biserial algebras | |
D. Happel: Algebras of finite global dimension | |
K. Igusa (with G. Todorov): Continuous Frobenius categories | |
D.A. Jorgensen: Triangle functors from generic hypersurfaces | |
Y. Kodama (with L. Williams): Combinatorics of KP solutions from the real Grassmannian | |
H. Krause: Mo | |
ISBN: | 9783642394850 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Abel Symposia, 2193-2808 : v8 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic , Differentiable dynamical systems |
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Call number: | SPRINGER-2013-9783642388309:ONLINE Show nearby items on shelf |
Title: | Progress and Challenges in Dynamical Systems [electronic resource] : Proceedings of the International Conference Dynamical Systems: 100 Years after Poincar, September 2012, Gijn, Spain |
Author(s): |
Santiago Ibez Jess S Prez del Ro Antonio Pumario J. ngel Rodrguez |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Springer eBooks |
ISBN: | 9783642388309 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v54 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional equations , Differentiable dynamical systems , Differential Equations , Systems theory |
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Call number: | SPRINGER-2013-9783642364334:ONLINE Show nearby items on shelf |
Title: | Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications [electronic resource] : Cetraro, Italy 2011, Editors: Paola Loreti, Nicoletta Anna Tchou |
Author(s): |
Yves Achdou Guy Barles Hitoshi Ishii Grigory L Litvinov |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Springer eBooks |
ISBN: | 9783642364334 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2074 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional equations , Differentiable dynamical systems , Differential equations, partial , Computer science Mathematics , Mathematical optimization |
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Call number: | SPRINGER-2013-9783642341007:ONLINE Show nearby items on shelf |
Title: | Continuous-Time Markov Jump Linear Systems [electronic resource] |
Author(s): |
Oswaldo L.V Costa Marcelo D Fragoso Marcos G Todorov |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | It has been widely recognized nowadays the importance of introducing mathematical models that take into account possible sudden changes in the dynamical behavior of high-integrity systems or a safety-critical system. Suchsystems can be found in aircr aft control, nuclear power stations, robotic manipulator systems, integrated communication networks and large-scale flexible structures for space stations, and are inherently vulnerable to abrupt changes intheir structures caused by component or interconn ection failures. In this regard, a particularly interesting class of models is the so-called Markov jump linear systems (MJLS), which have been used in numerous applications includingrobotics, economics and wireless communication. Combining probability an d operator theory, the present volume provides a unified and rigorous treatment of recent results in control theory of continuous-time MJLS. This unique approachis of great interest to experts working in the field of linear systems with Markovian jump par ameters or in stochastic control. The volume focuses on one of the few cases of stochastic control problems with an actual explicit solutionand offers material well-suited to coursework, introducing students to an interesting and active research area. The book is addressed to researchers working in control and signal processing engineering. Prerequisites include a solidbackground in classical linear control theory, basic familiarity with continuous-time Markov chains and probability theory, and some eleme ntary knowledge of operator theory |
Note: | Springer eBooks |
Contents: | 1.Introduction |
2.A Few Tools and Notations | |
3.Mean Square Stability | |
4.Quadratic Optimal Control with Complete Observations | |
5.H2 Optimal Control With Complete Observations | |
6.Quadratic and H2 Optimal Control with Partial Observations | |
7.Best Linear Filter with Unknown (x(t), (t)) | |
8.H_$infty$ Control | |
9.Design Techniques | |
10.Some Numerical Examples | |
A.Coupled Differential and Algebraic Riccati Equations | |
B.The Adjoint Operator and Some Auxiliary Results | |
References | |
Notation and Conventions | |
Index | |
ISBN: | 9783642341007 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Probability and Its Applications, 1431-7028 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Operator theory , Systems theory , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9783642338175:ONLINE Show nearby items on shelf |
Title: | Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations [electronic resource] |
Author(s): |
Valery V Kozlov Stanislav D Furta |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunovs first method. A prominent place is given toasymptotic solutions that t end to an equilibrium position, especially in the strongly nonlinear case, where the existence of such solutions cant be inferred on the basis of the first approximation alone. The book is illustrated witha large number of concrete examples of systems in which the presence of a particular solution of a certain class is related to special properties of the systems dynamic behavior. It is a book for students and specialists who workwith dynamical systems in the fields of mechanics, mathematics, and theoreti cal physics |
Note: | Springer eBooks |
Contents: | Preface |
Semi | |
quasihomogeneous systems of ordinary differential equations | |
2. The critical case of purely imaginary kernels | |
3. Singular problems | |
4. The inverse problem for the Lagrange theorem on the stability of equilibrium and other related problems | |
Appendix A. Nonexponential asymptotic solutions of systems of functional | |
differential equations | |
Appendix B. Arithmetic properties of the eigenvalues of the Kovalevsky matrix and conditions for the nonintegrability of semi | |
quasihomogeneous systems of ordinary dierential equations | |
Bibliography | |
ISBN: | 9783642338175 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Differential Equations , Mathematical physics |
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Call number: | SPRINGER-2013-9783642331312:ONLINE Show nearby items on shelf |
Title: | Quasi-Stationary Distributions [electronic resource] : Markov Chains, Diffusions and Dynamical Systems |
Author(s): |
Pierre Collet Servet Martnez Jaime San Martn |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Main concepts of quasi-stationary distributions (QSDs) for killed processes are the focus of the present volume. For diffusions, the killing is at the boundary and for dynamical systems there is a trap. The authors present theQSDs as the ones that al low describing the long-term behavior conditioned to not being killed. Studies in this research area started with Kolmogorov and Yaglom and in the last few decades have received a great deal of attention. Theauthors provide the exponential distribution pr operty of the killing time for QSDs, present the more general result on their existence and study the process of trajectories that survive forever. For birth-and-death chains anddiffusions, the existence of a single or a continuum of QSDs is described. Th ey study the convergence to the extremal QSD and give the classification of the survival process. In this monograph, the authors discuss Gibbs QSDs forsymbolic systems and absolutely continuous QSDs for repellers. The findings described are relevant to re searchers in the fields of Markov chains, diffusions, potential theory, dynamical systems, and in areas where extinction is acentral concept. The theory is illustrated with numerous examples. The volume uniquely presents the distribution behavior of indiv iduals who survive in a decaying population for a very long time. It also provides the background forapplications in mathematical ecology, statistical physics, computer sciences, and economics |
Note: | Springer eBooks |
Contents: | 1.Introduction |
2.Quasi | |
stationary Distributions: General Results | |
3.Markov Chains on Finite Spaces | |
4.Markov Chains on Countable Spaces | |
5.Birth and Death Chains | |
6.Regular Diffusions on [0,) | |
7.Infinity as Entrance Boundary | |
8.Dynamical Systems | |
References | |
Index | |
Table of Notations | |
Citations Index. | |
ISBN: | 9783642331312 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Probability and Its Applications, 1431-7028 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Differential equations, partial , Genetics Mathematics , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9783642329067:ONLINE Show nearby items on shelf |
Title: | Stability and Bifurcation Theory for Non-Autonomous Differential Equations [electronic resource] : Cetraro, Italy 2011, Editors: Russell Johnson, Maria Patrizia Pera |
Author(s): |
Anna Capietto Peter Kloeden Jean Mawhin Sylvia Novo Rafael Ortega |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Springer eBooks |
ISBN: | 9783642329067 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2065 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional equations , Differentiable dynamical systems , Differential Equations |
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Call number: | SPRINGER-2013-9783319012889:ONLINE Show nearby items on shelf |
Title: | Invariance Entropy for Deterministic Control Systems [electronic resource] : An Introduction |
Author(s): |
Christoph Kawan |
Date: | 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible networktopology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state spaceinvariant by means of a symbolic coder-contro ller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinearstabilization. IEEE Trans. Automat. Control 49 (2004), 15851597). The b ook presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents.While both discrete-time and continuous-time systems are treated, the emphasis lies on systems gi ven by differential equations |
Note: | Springer eBooks |
Contents: | Basic Properties of Control Systems |
Introduction to Invariance Entropy | |
Linear and Bilinear Systems | |
General Estimates | |
Controllability, Lyapunov Exponents, and Upper Bounds | |
Escape Rates and Lower Bounds | |
Examples | |
Notation | |
Bibliography | |
Index | |
ISBN: | 9783319012889 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2089 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Systems theory |
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Call number: | SPRINGER-2013-9783319008288:ONLINE Show nearby items on shelf |
Title: | The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lvy Noise [electronic resource] |
Author(s): |
Arnaud Debussche Michael Hgele Peter Imkeller |
Date: | 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in aseparating manifold wi th several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attractiondepend polynomially on the noise intensity i n the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamicbehavior of a finite-state Markov chain switching between the stabl e states |
Note: | Springer eBooks |
Contents: | Introduction |
The fine dynamics of the Chafee | |
Infante equation | |
The stochastic Chafee | |
Infante equation | |
The small deviation of the small noise solution | |
Asymptotic exit times | |
Asymptotic transition times | |
Localization and metastability | |
The source of stochastic models in conceptual climate dynamics | |
ISBN: | 9783319008288 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2085 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Differential equations, partial , Distribution (Probability theory) |
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Title: | Dimension Theory of Hyperbolic Flows [electronic resource] |
Author(s): |
Lus Barreira |
Date: | 2013 |
Publisher: | Heidelberg : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The dimension theory of dynamical systems has progressively developed, especially over the last two decades, into an independent and extremely active field of research. Its main aim is to study the complexity of sets and measuresthat are invariant un der the dynamics. In particular, it is essential to characterizing chaotic strange attractors. To date, some parts of the theory have either only been outlined, because they can be reduced to the case of maps, orare too technical for a wider audience. In this respect, the present monograph is intended to provide a comprehensive guide. Moreover, the text is self-contained and with the exception of some basic results in Chapters 3 and 4, all theresults in the book include detailed proofs. The book is inten ded for researchers and graduate students specializing in dynamical systems who wish to have a sufficiently comprehensive view of the theory together with a workingknowledge of its main techniques. The discussion of some open problems is also included in the hope that it may lead to further developments. Ideally, readers should have some familiarity with the basic notions and results of ergodictheory and hyperbolic dynamics at the level of an introductory course in the area, though the initial chapters al so review all the necessary material |
Note: | Springer eBooks |
Contents: | Introduction |
Suspension Flows | |
Hyperbolic Flows | |
Pressure and Dimension | |
Dimension of Hyperbolic Sets | |
Pointwise Dimension and Applications | |
Suspensions over Symbolic Dynamics | |
Multifractal Analysis of Hyperbolic Flows | |
Entropy Spectra | |
Multidimensional Spectra | |
Dimension Spectra | |
References | |
Index | |
ISBN: | 9783319005485 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Differentiable dynamical systems |
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Call number: | SPRINGER-2013-9783319001258:ONLINE Show nearby items on shelf |
Title: | Progress in Partial Differential Equations [electronic resource] : Asymptotic Profiles, Regularity and Well-Posedness |
Author(s): |
Michael Reissig Michael Ruzhansky |
Date: | 2013 |
Publisher: | Heidelberg : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partialdifferential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society. This volume is addressed to graduate studentsat various levels as well as researchers in partial differential equations and related fields. The reader will find this an excellent resource of both introductory and advanced material. The key topics are: Linear hyperbolicequations and systems (scattering, symmetrisers) Non-linear wave models ( global existence, decay estimates, blow-up) Evolution equations (control theory, well-posedness, smoothing) Elliptic equations (uniqueness,non-uniqueness, positive solutions) Special models from applications (Kirchhoff equation, Zakharov-Kuznetsov equa tion, thermoelasticity) |
Note: | Springer eBooks |
Contents: | Preface |
Global Existence and Energy Decay of Solutions for a Nondissipative Wave Equation with a Time | |
Varying Delay Term | |
Non | |
uniqueness and uniqueness in the Cauchy problem of elliptic and backward | |
parabolic equations | |
On internal regularity of solutions to the initial value problem for the ZakharovKuznetsov equation | |
Singular semilinear elliptic equations with subquadratic gradient terms | |
On the parabolic regime of a hyperbolic equation with weak dissipation: the coercive case | |
H well | |
posedness for degenerate p | |
evolution models of higher order with time | |
dependent coefficien | |
ISBN: | 9783319001258 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v44 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2013-9783034806978:ONLINE Show nearby items on shelf |
Title: | Chaos [electronic resource] : Poincar Seminar 2010 |
Author(s): |
Bertrand Duplantier Stphane Nonnenmacher Vincent Rivasseau |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This twelfth volume in the Poincar Seminar Series presents a complete and interdisciplinary perspective on the concept of Chaos, both in classical mechanics in its deterministic version, and in quantum mechanics. This bookexpounds some of the most wi de ranging questions in science, from uncovering the fingerprints of classical chaotic dynamics in quantum systems, to predicting the fate of our own planetary system. Its seven articles are also highlypedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a complete description by the mathematician . Ghys of the paradigmatic Lorenz attractor, and of the famed Lorenz butterfly effect asit is understood today, illuminating the fundamental mathematical issues at p lay with deterministic chaos a detailed account by the experimentalist S. Fauve of the masterpiece experiment, the von Krmn Sodium or VKS experiment,which established in 2007 the spontaneous generation of a magnetic field in a strongly turbulent flow, inc luding its reversal, a model of Earths magnetic field a simple toy model by the theorist U. Smilansky the discreteLaplacian on finite d-regular expander graphs which allows one to grasp the essential ingredients of quantum chaos, including its fundament al link to random matrix theory a review by the mathematical physicists P. Bourgade andJ.P. Keating, which illuminates the fascinating connection between the distribution of zeros of the Riemann -function and the statistics of eigenvalues of random unitar y matrices, which could ultimately provide a spectralinterpretation for the zeros of the -function, thus a proof of the celebrated Riemann Hypothesis itself an article by a pioneer of experimental quantum chaos, H-J. Stckmann, who shows in detail how expe riments on the propagationof microwaves in 2D or 3D chaotic cavities beautifully verify theoretical predictions a thorough presentation by the mathematical physicist S. Nonne |
Note: | Springer eBooks |
Contents: | Foreword |
1 tienne Ghys, The Lorenz Attractor, a Paradigm for Chaos | |
2 Stphan Fauve, Chaotic Dynamos Generated by Fully Turbulent Flows | |
3 Uzy Smilansky, Discrete Graphs | |
A Paradigm Model for Quantum Chaos | |
4 Paul Bourgade and Jonathan P. Keating, Quantum Chaos, Random Matrix Theory, and the Riemann | |
function | |
5 Hans | |
Jrgen Stckmann, Chaos in Microwave Resonators | |
6 Stphane Nonnenmacher, Anatomy of Quantum Chaotic Eigenstates | |
7 Jacques Laskar, Is the Solar System Stable? | |
ISBN: | 9783034806978 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematical Physics, 1544-9998 : v66 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Number theory |
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Call number: | SPRINGER-2013-9783034804813:ONLINE Show nearby items on shelf |
Title: | Complex Kleinian Groups [electronic resource] |
Author(s): |
Angel Cano Juan Pablo Navarrete Jos Seade |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph lays down the foundations of the theory of complex Kleinian groups, a newborn area of mathematics whose origin can be traced back to the work of Riemann, Poincar, Picard and many others. Kleinian groupsare, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions,there is a dichotomy: Should we look at conformal automorp hisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In thefirst case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition in the second, about an area of mathematics that is still in its infancy, and this is the focus ofstudy in this monograph. It brings together several important areas of mathematics, e.g. classical Kleini an group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Acknowledgments | |
1 A glance of the classical theory | |
2 Complex hyperbolic geometry | |
3 Complex Kleinian groups | |
4 Geometry and dynamics of automorphisms of P2C | |
5 Kleinian groups with a control group | |
6 The limit set in dimension two | |
7 On the dynamics of discrete subgroups of PU(n,1) | |
8 Projective orbifolds and dynamics in dimension two | |
9 Complex Schottky groups | |
10 Kleinian groups and twistor theory | |
Bibliography | |
Index. | |
ISBN: | 9783034804813 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v303 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Differentiable dynamical systems , Differential equations, partial |
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Call number: | SPRINGER-2013-9783034804516:ONLINE Show nearby items on shelf |
Title: | Recent Trends in Dynamical Systems [electronic resource] : Proceedings of a Conference in Honor of Jrgen Scheurle |
Author(s): |
Andreas Johann Hans-Peter Kruse Florian Rupp Stephan Schmitz |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book presents the proceedings of a conference on dynamical systems held in honor of Jrgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews ofthe current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: - Stability and bifurcation -Geometric mechanics and control theory-Invariant manifolds, attractors and chaos -Flui d mechanics and elasticity -Perturbations and multiscale problems - Hamiltonian dynamics and KAM theory Researchers and graduate students in dynamical systems and related fields,including engineering, will benefit from the articles presented in this volum e. Contributors: Fred C. Adams Henk W. Broer Anthony M. Bloch Tomas Caraballo David R.J. Chillingworth Freddy Dumortier Messoud Efendiev Tor Fl Peter A.Giesl Christoph Glocker Alexandra Goeke John Guckenheimer Sigurdur Hafstein Heinz Hanmann Darryl D. Hol m Hany A. Hosham Eric W. Justh Peter E. Kloeden P. S. Krishnaprasad Martin Kruk Tassilo Kpper Alexander Mielke JamesMontaldi Philip J. Morrison Jonathan Munn Arne B. Nordmark Marius Paicu Tudor S. Ratiu Genevive Raugel Sebastian Reich Michael Renardy Flor ian H.-H. Rupp Bjrn Sandstede Samuel N. Stechmann Tadashi Tokieda Andr VanderbauwhedeSebastian Walcher Daniel Weiss Clemens Woywod Jiangong You Fumin Zhang Anna Zhigun Johannes Zimmer |
Note: | Springer eBooks |
Contents: | Part I Stability, Bifurcation & Perturbations |
Part II Hamiltonian Dynamics, Geometric Mechanics & Control Theory | |
Part III Continuum Mechanics: Solids, Fluids and other Materials | |
ISBN: | 9783034804516 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v35 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems |
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Call number: | SPRINGER-2013-9783034803595:ONLINE Show nearby items on shelf |
Title: | Time [electronic resource] : Poincar Seminar 2010 |
Author(s): |
Bertrand Duplantier |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This eleventh volume in the Poincar Seminar Series presents an interdisciplinary perspective on the concept of Time, which poses some of the most challenging questions in science. Five articles, written by the Fields medalistC. Villani, the two outst anding theoretical physicists T. Damour and C. Jarzynski, the leading experimentalist C. Salomon, and the famous philosopher of science H. Price, describe recent developments related to the mathematical,physical, experimental, and philosophical facets of this fascinating concept. These articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a description of themanifold fundamental physical issues in play with time, in particular with the changes of perspective implied by Special and General Relativity a mathematically precise discussion of irreversibility and entropy in the context ofBoltzmann's and Vlasov's equations a thorough survey of the recently developed thermodynamics at the nanos cale, the scale most relevant to biological physics a description of the new cold atom space clockPHARAO to beinstalled in 2015 onboard the International Space Station, which will allow a test of Einstein's gravitational shift with a record precision of 2 10-6, and enable a test of the stability over time of the fundamental constants ofphysics, an issue first raised by Dirac in 1937 and last, but not least, a logical and clarifying philosophical discussion of Time's arrow, a phrase first coined by Edding ton in 1928 in a challenge to physics to resolve thepuzzle of the time-asymmetry of our universe, and echoed here in a short pome en prose by C. de Mitry. This book should be of broad general interest to physicists, mathematicians, and philosophers |
Note: | Springer eBooks |
Contents: | Foreword |
Time and Relativity, Thibault Damour | |
(Ir)reversibility and Entropy, Cdric Villani | |
(Ir)rversibilit et entropie, Cdric Villani | |
Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale, Christopher Jarzynski | |
Time Measurement in the XXIst Century, Christophe Salomon | |
Times Arrow and Eddingtons Challenge, Huw Price | |
Image of Times Irreversibility, Catherine de Mitry | |
Image de l'irrversibilit du Temps, Catherine de Mitry | |
ISBN: | 9783034803595 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematical Physics : v63 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Distribution (Probability theory) , Quantum theory , Mechanics |
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Call number: | SPRINGER-2013-9781461475828:ONLINE Show nearby items on shelf |
Title: | Dynamics of Information Systems: Algorithmic Approaches [electronic resource] |
Author(s): |
Alexey Sorokin Panos M Pardalos |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Dynamics of Information Systems: Algorithmic Approaches presents recent developments and results found by participants of the Fourth International Conference on the Dynamics of Information Systems, which took place at theUniversity of Florida, Gaines ville FL, USA on February 2022, 2012. The purpose of this conference was to bring together scientists and engineers from industry, government, and universities to exchange knowledge and results in abroad range of topics relevant to the theory and practice of the dynamics of information systems. Dynamics of Information plays an increasingly critical role in our society. The influence of information on social, biological, genetic,and military systems must be better understood to achieve large advances in th e capability and understanding of these systems. Applications are widespread and include: detection of terrorist networks, design of highly efficientbusinesses, computer networks, quantum entanglement, genome modeling, multi-robotic systems, and industria l and manufacturing safety. The book contains state-of-the-art work on theory and practice relevant to the dynamics ofinformation systems. It covers algorithmic approaches to numerical computations with infinite and infinitesimal numbers presents importan t problems arising in service-oriented systems, such as dynamic composition and analysis ofmodern service-oriented information systems and estimation of customer service times on a rail network from GPS data addresses the complexity of the problems arisin g in stochastic and distributed systems and discusses modulatingcommunication for improving multi-agent learning convergence. Network issuesin particular minimum-risk maximum-clique problems, vulnerability of sensor networks, influence diffusion, communit y detection, and link prediction insocial network analysis, as well as a comparative analysis of algorithms for transmission network expansion planningare described in later chapters |
Note: | Springer eBooks |
Contents: | Numerical computations with infinite and infinitesimal numbers: Theory and applications (Y.D. Sergeyev) |
Dynamic Composition and Analysis of modern service | |
oriented information systems (H. Abdulrab, E. Babkin, and J. Doucy) | |
Estimating Customer Service Times on a Rail Network from GPS Data (S. Spanton) | |
A Risk | |
Averse Game | |
Theoretic Approach to Distributed Control (K. Pham and M. Pachter) | |
Static Teams and Stochastic Games (M. Pachter and K. Pham) | |
A Framework for Coordination in Distributed Stochastic Systems: Output Feedback and Performance Risk Aversion (K. Pham) | |
Modulating Comm | |
ISBN: | 9781461475828 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v51 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Systems theory , Operations research |
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Call number: | SPRINGER-2013-9781461473336:ONLINE Show nearby items on shelf |
Title: | Differential and Difference Equations with Applications [electronic resource] : Contributions from the International Conference on Differential & Difference Equations and Applications |
Author(s): |
Sandra Pinelas Michel Chipot Zuzana Dosla |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Springer eBooks |
ISBN: | 9781461473336 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v47 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional equations , Differentiable dynamical systems , Integral equations , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2013-9781461472766:ONLINE Show nearby items on shelf |
Title: | Mathematics for the Life Sciences [electronic resource] : Calculus, Modeling, Probability, and Dynamical Systems |
Author(s): |
Glenn Ledder |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Mathematics for the Life Sciences provides present and future biologists with the mathematical concepts and tools needed to understand and use mathematical models and read advanced mathematical biology books. It presentsmathematics in biological cont exts, focusing on the central mathematical ideas, and providing detailed explanations. The author assumes no mathematics background beyond algebra and precalculus. Calculus is presented as aone-chapter primer that is suitable for readers who have not stud ied the subject before, as well as readers who have taken a calculus course and need a review. This primer is followed by a novel chapter on mathematical modeling thatbegins with discussions of biological data and the basic principles of modeling. The rem ainder of the chapter introduces the reader to topics in mechanistic modeling (deriving models from biological assumptions) and empiricalmodeling (using data to parameterize and select models). The modeling chapter contains a thorough treatment of key ide as and techniques that are often neglected in mathematics books. It also provides the reader with a sophisticatedviewpoint and the essential background needed to make full use of the remainder of the book, which includes two chapters on probability and it s applications to inferential statistics and three chapters on discrete and continuousdynamical systems. The biological content of the book is self-contained and includes many basic biology topics such as the genetic code, Mendelian genetics, population d ynamics, predator-prey relationships, epidemiology, andimmunology. The large number of problem sets include some drill problems along with a large number of case studies. The latter are divided into step-by-step problems and sorted into the appropriate se ction, allowing readers togradually develop complete investigations from understanding the biological assumptions to a complete analysis |
Note: | Springer eBooks |
Contents: | A Brief Summary of Calculus |
Mathematical Modeling | |
Probability Distributions | |
Working with Probability | |
Dynamics of Single Populations | |
Discrete Dynamical Systems | |
Continuous Dynamical Systems | |
Index | |
ISBN: | 9781461472766 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Undergraduate Texts in Mathematics and Technology, 1867-5506 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Life sciences , Differentiable dynamical systems |
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Call number: | SPRINGER-2013-9781461469957:ONLINE Show nearby items on shelf |
Title: | Spectral and Dynamical Stability of Nonlinear Waves [electronic resource] |
Author(s): |
Todd Kapitula Keith Promislow |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory andapplication. The book isolate s and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbitalstability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functionalanalytic point of view, including essential and absolute spectra, and devel ops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems iscarefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of theEvans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative ex amples. The book is intended for first or second year graduate students in mathematics, or those with equivalentmathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position tounderstand and contribute to current research in nonlinear stability |
Note: | Springer eBooks |
Contents: | Introduction |
Background material and notation | |
Essential and absolute spectra | |
Dynamical implications of spectra: dissipative systems | |
Dynamical implications of spectra: Hamiltonian systems | |
Dynamical implications of spectra: Hamiltonian systems | |
Point spectrum: reduction to finite | |
rank eigenvalue problems | |
Point spectrum: linear Hamiltonian systems | |
The Evans function for boundary value problems | |
The Evans function for Sturm | |
Liouville operators on the real line | |
The Evans function for nth | |
order operators on the real line | |
Index | |
References | |
ISBN: | 9781461469957 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied Mathematical Sciences, 0066-5452 : v185 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Differential equations, partial |
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Call number: | SPRINGER-2013-9781461469926:ONLINE Show nearby items on shelf |
Title: | Bifurcation Theory of Functional Differential Equations [electronic resource] |
Author(s): |
Shangjiang Guo Jianhong Wu |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise verynaturally in economics, life sciences and engineering and the study of FDEs hasbeen a major source of inspira tion for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcationphenomena of FDEs depending on parameters. The book aims to be self-contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal formsand center manifold reduction. This material was used in graduate courses on fu nctional differential equations at Hunan University (China) and York University (Canada) |
Note: | Springer eBooks |
ISBN: | 9781461469926 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied Mathematical Sciences, 0066-5452 : v184 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional equations , Differentiable dynamical systems , Differential Equations |
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Call number: | SPRINGER-2013-9781461463481:ONLINE Show nearby items on shelf |
Title: | Studies in Phase Space Analysis with Applications to PDEs [electronic resource] |
Author(s): |
Massimo Cicognani Ferruccio Colombini Daniele Del Santo |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This collection of original articles and surveys, emerging from a 2011 conference in Bertinoro, Italy,addresses recent advances in linear and nonlinear aspects of the theory of partial differential equations (PDEs). Phase spaceanalysis methods, also known as microlocal analysis, have continued to yield striking results over the past years and are now one of the main tools of investigation of PDEs. Their role in many applications to physics, including quantumand spectral theory, is equally important. Key topics addressed in this volume include: *general theory of pseudodifferential operators *Hardy-type inequalities *linear and non-linear hyperbolic equations and systems *Schrdingerequations *water-wave equations *Euler-Poisson systems *Navier-Stokes equations *heat and parabolic equations Various levels of graduate students, along with researchers in PDEs and related fields, will find this book to be anexcellent resource. Contributors T. Alazard P.I. Naumkin J.-M. BonyF. Nicola N.Burq T. Nishitani C. Cazacu T. Okaji J.-Y. Chemin M.Paicu E. CorderoA. Parmeggiani R. Danchin V. Petkov I.Gallagher M. Reissig T. Gramchev L. Robbiano N. Hayashi L.Rodino J. HuangM. Ruzhanky D. Lannes J.-C. Saut F. Linares |
Note: | Springer eBooks |
Contents: | Preface |
The water | |
waves equations: from Zakharov to Euler | |
On the characterization of pseudodifferential operators (old and new) | |
Improved multipolar Hardy inequalities | |
The role of spectral anisotropy in the resolution of the three | |
dimensional Navier | |
Stokes equations | |
Schrdinger equations in modulation spaces | |
New maximal regularity results for the heat equation in exterior domains, and applications | |
Cauchy problem for some 22 hyperbolic systems of pseudo | |
differential equations with nondiagonalisable principal part | |
Scattering problem for quadratic nonlinear Klein | |
Gordon eq | |
ISBN: | 9781461463481 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Nonlinear Differential Equations and Their Applications : v84 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Differentiable dynamical systems , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2013-9781461451556:ONLINE Show nearby items on shelf |
Title: | Turbulence and Self-Organization [electronic resource] : Modeling Astrophysical Objects |
Author(s): |
Mikhail Ya Marov Aleksander V Kolesnichenko |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book focuses on the development of continuum models of natural turbulent media. It providesa theoretical approach tothesolutions ofdifferent problems related to the formation, structure and evolution of astrophysicaland geophysical objects. A st ochastic modeling approach is used in the mathematical treatment of these problems, which reflects self-organization processes in open dissipative systems. The authors also consider examples of ordering forvarious objects in space throughout their evoluti onary processes. This volume is aimed at graduate students and researchers in the fields of mechanics, astrophysics, geophysics, planetary and space science |
Note: | Springer eBooks |
Contents: | Turbulent Chaos and Self |
organization in Space and Natural Environments | |
Basics of Mathematical Modeling of Reactive Gas Mixtures | |
Closed System of Hydrodynamic Equations for the Description of Turbulent Motion of Multicomponent Media | |
Differential Models of Closure of the Averaged Hydrodynamic Equations for the Turbulent Chemically | |
active Continuous Medium | |
Stochastic | |
thermodynamic Modeling of the Developed Structural Turbulence | |
Self | |
organization of the Developed Turbulence and Mechanisms of Coherent Structure Formation | |
Basics of Heterogeneous Mechanics with Applications to Accret | |
ISBN: | 9781461451556 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Astrophysics and Space Science Library, 0067-0057 : v389 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Differentiable dynamical systems |
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Call number: | SPRINGER-2013-9781461450795:ONLINE Show nearby items on shelf |
Title: | Linear-Quadratic Controls in Risk-Averse Decision Making [electronic resource] : Performance-Measure Statistics and Control Decision Optimization |
Author(s): |
Khanh D Pham |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Linear-Quadratic Controls in Risk-Averse Decision Making cuts across control engineering (control feedback and decision optimization) and statistics (post-design performance analysis) with a common theme: reliability increaseseen from the responsive angle of incorporating and engineering multi-level performance robustness beyond the long-run average performance into control feedback design and decision making and complex dynamic systems from the start.This monograph provides a complete description o f statistical optimal control (also known as cost-cumulant control) theory. In control problems and topics, emphasis is primarily placed on major developments attained and explicitconnections between mathematical statistics of performance appraisals and d ecision and control optimization. Chapter summaries shed light on the relevance of developed results, which makes this monograph suitable for graduate-levellectures in applied mathematics and electrical engineering with systems-theoretic concentration, el ective study or a reference for interested readers, researchers, and graduate students who are interested in theoretical constructs anddesign principles for stochastic controlled systems. |
Note: | Springer eBooks |
ISBN: | 9781461450795 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Optimization, 2190-8354 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Computer science , Mathematical optimization , Mathematical statistics |
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Call number: | SPRINGER-2013-9781461445814:ONLINE Show nearby items on shelf |
Title: | Attractors for infinite-dimensional non-autonomous dynamical systems [electronic resource] |
Author(s): |
Alexandre N Carvalho Jos A Langa James C Robinson |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book treats the theory of pullback attractors for non-autonomous dynamical systems. While the emphasis is on infinite-dimensional systems, the results are also applied to a variety of finite-dimensional examples. Thepurpose of the book is to pr ovide a summary of the current theory, starting with basic definitions and proceeding all the way to state-of-the-art results. As such it is intended as a primer for graduate students, and a reference formore established researchers in the field. The bas ic topics are existence results for pullback attractors, their continuity under perturbation, techniques for showing that their fibres are finite-dimensional, and structural resultsfor pullback attractors for small non-autonomous perturbations of gradient systems (those with a Lyapunov function). The structural results stem from a dynamical characterisation of autonomous gradient systems, which shows inparticular that such systems are stable under perturbation. Application of the structural results relies on the continuity of unstable manifolds under perturbation, which in turn is based on the robustness of exponential dichotomies: aself-contained development of these topics is given in full. After providing all the necessary theory the book treats a numb er of model problems in detail, demonstrating the wide applicability of the definitions and techniquesintroduced: these include a simple Lotka-Volterra ordinary differential equation, delay differential equations, the two-dimensional Navier-Stokes equatio ns, general reaction-diffusion problems, a non-autonomous version of theChafee-Infante problem, a comparison of attractors in problems with perturbations to the diffusion term, and a non-autonomous damped wave equation. Alexandre N. Carvalho is a Professo r at the University of Sao Paulo, Brazil. Jos A.Langa is a Profesor Titular at the University of Seville, Spain. James C. Robinson is a Professor at the University of Warwick, UK |
Note: | Springer eBooks |
Contents: | The pullback attractor |
Existence results for pullback attractors | |
Continuity of attractors | |
Finite | |
dimensional attractors | |
Gradient semigroups and their dynamical properties | |
Semilinear Differential Equations | |
Exponential dichotomies | |
Hyperbolic solutions and their stable and unstable manifolds | |
A non | |
autonomous competitive Lotka | |
Volterra system | |
Delay differential equations | |
The NavierStokes equations with non | |
autonomous forcing | |
Applications to parabolic problems | |
A non | |
autonomous ChafeeInfante equation | |
Perturbation of diffusion and continuity of attractors w | |
ISBN: | 9781461445814 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied Mathematical Sciences, 0066-5452 : v182 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Differential equations, partial , Cell aggregation Mathematics |
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Call number: | SPRINGER-2013-9781461445234:ONLINE Show nearby items on shelf |
Title: | Infinite Dimensional Dynamical Systems [electronic resource] |
Author(s): |
John Mallet-Paret Jianhong Wu Yingfie Yi Huaiping Zhu |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic and hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differentialequations, and stochas tic differential equations. Infinite dimensional dynamical systems are generated by equations describing the evolution in time of systems whose status must be depicted in infinite dimensional phase spaces.Studying the long-term behaviors of such systems i s important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among the major sources of motivation and applications of newdevelopments in nonlinear analysis and other mathematical theories. The theory of infinite dimensional dynamical systems has also increasingly important applications in the physical, chemical and life sciences. This book collects 19papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Syste ms held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from Universityof Minnesota on the occasion of his 70th birthday, this collection reflects his pioneering work and influence in core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifoldstheory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows |
Note: | Springer eBooks |
Contents: | Preface |
Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems (J. Hale, G. Raugel) | |
Spectral Theory for Forward Nonautonomus Parabolic Equations and Applications (J. Mierczynski, W. Shen) | |
A Dynamical Systems Approach to Traveling Wave Solutions for Liquid/Vapor Phase Transition (H. Fan, X. Lin) | |
Instability of Radially | |
Symmetric Spikes in Systems with Conserved Quantity (A. Pogan, A. Scheel) | |
Global Hopf Bifurcation Analysis of a Neuron Network Model with Time Delays (M. Li, J. Wei) | |
Instability of Low Density Supersonic Waves of a Viscous Isentropic Gas Flow | |
ISBN: | 9781461445234 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Fields Institute Communications, 1069-5265 : v64 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2013-9781461444817:ONLINE Show nearby items on shelf |
Title: | Exterior Billiards [electronic resource] : Systems with Impacts Outside Bounded Domains |
Author(s): |
Alexander Plakhov |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | A billiard is a dynamical system in which a point particle alternates between free motion and specular reflections fromthe boundaryof a domain.Exterior Billiards presents billiards in the complement of domains and theirapplications in aerodynamics an d geometrical optics. This book distinguishes itself from existing literature by presenting billiard dynamics outside bounded domains, including scattering, resistance, invisibility andretro-reflection. It begins with an overview of the mathematical notat ions used throughout the book and a brief review of the main results. Chapters 2 and 3 are focused on problems of minimal resistance and Newtons problem inmedia with positive temperature. In chapters 4 and 5, scattering of billiards bynonconvex and rough domains is characterized and some related special problems of optimal mass transportation are studied. Applications in aerodynamicsare addressed next and problems of invisibility and retro-reflection within the framework of geometric optics conclude the t ext. The book will appeal to mathematicians working in dynamical systems and calculus of variations.Specialists working in the areas of applications discussed will also find it useful |
Note: | Springer eBooks |
ISBN: | 9781461444817 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Mathematical optimization |
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Call number: | SPRINGER-2013-9781461421764:ONLINE Show nearby items on shelf |
Title: | Fractal Geometry, Complex Dimensions and Zeta Functions [electronic resource] : Geometry and Spectra of Fractal Strings |
Author(s): |
Michel L Lapidus Machiel van Frankenhuijsen |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings that is, one-dimensional drums with fractal boundary. This second edition of Fractal Geometry,Complex Dimensions and Ze ta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, complex analysis, distribution theory, and mathematical physics. The significantstudies and problems illuminated in this work ma y be used in a classroom setting at the graduate level. Key Features include: The Riemann hypothesis is given a natural geometric reformulation in the context ofvibrating fractal strings Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal Examples of such explic it formulas include a Prime Orbit Theorem witherror term for self-similar flows, and a geometric tube formula The method of Diophantine approximation is used to study self-similar strings and flows Analytical and geometric methods are used toobtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. Thefinal chapter (13) is new to the s econd edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: Thebook is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theor |
Note: | Springer eBooks |
Contents: | Preface |
Overview | |
Introduction | |
1. Complex Dimensions of Ordinary Fractal Strings | |
2. Complex Dimensions of Self | |
Similar Fractal Strings | |
3. Complex Dimensions of Nonlattice Self | |
Similar Strings | |
4. Generalized Fractal Strings Viewed as Measures | |
5. Explicit Formulas for Generalized Fractal Strings | |
6. The Geometry and the Spectrum of Fractal Strings | |
7. Periodic Orbits of Self | |
Similar Flows | |
8. Fractal Tube Formulas | |
9. Riemann Hypothesis and Inverse Spectral Problems | |
10. Generalized Cantor Strings and their Oscillations | |
11. Critical Zero of Zeta Functions | |
12 F | |
ISBN: | 9781461421764 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Functional analysis , Global analysis , Differential equations, partial , Number theory |
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