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Call number: | QA372.G56::1994 Show nearby items on shelf |

Title: | Stability, instability, and chaos: An introduction to the theory of nonlinear differential equations |

Author(s): |
Paul Glendinning |

Date: | 1994 |

Publisher: | New York : Cambridge University Press |

Size: | 388 p. |

Contents: | Solving differential equations -- Existence and uniqueness theorems -- Phase space and flows -- Limit sets and trajectories -- Stability -- Definitions of stability -- Liapounov functions -- Strong linear stability -- Orbital stability -- Bounding functions -- Non-autonomous equations -- Linear Differential Equations -- Autonomous linear differential equations -- $t Normal forms -- $t Invariant manifolds -- Geometry of phase space -- Floquet Theory -- Linearization and Hyperbolicity -- Poincare's Linearization Theorem -- Hyperbolic stationary points and the stable manifold theorem -- Persistence of hyperbolic stationary points -- Structural stability -- Nonlinear sinks -- The proof of the stable manifold theorem -- Two Dimensional Dynamics -- Linear systems in R[superscript 2] -- The effect of nonlinear terms -- Rabbits and sheep -- Trivial linearization -- The Poincare index -- Dulac's criterion -- Pike and eels -- The Poincare-Bendixson Theorem -- Decay of large amplitudes -- Periodic Orbits -- Linear and nonlinear maps -- Return maps -- Floquet Theory revisited -- Periodically forced differential equations -- Normal forms for maps in R[superscript 2] -- Perturbation Theory -- Asymptotic expansions -- The method of multiple scales -- Multiple scales for forced oscillators: complex notation -- Higher order terms -- Interlude -- Nearly Hamiltonian systems -- Resonance in the Mathieu equation -- Parametric excitation in Mathieu equations -- Frequency locking -- Hysteresis -- Asynchronous quenching -- Subharmonic resonance. |

ISBN: | 0521415535 |

Series: | Cambridge texts in applied mathematics |

Keywords: | Differential equations, Nonlinear. , Bifurcation theory. , Chaotic behavior in systems. |

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Location: | MAIN |

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