Introduction to Applied Nonlinear Dynamical Systems and Chaos

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ISBN: 978-0-387-00177-7 (Print) 978-0-387-21749-9 (Online)

Table of contents (35 chapters)

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  1. No Access

    Book Chapter

    Pages 1-4

    Introduction

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    Book Chapter

    Pages 5-19

    Equilibrium Solutions, Stability, and Linearized Stability

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    Book Chapter

    Pages 20-27

    Liapunov Functions

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    Book Chapter

    Pages 28-70

    Invariant Manifolds: Linear and Nonlinear Systems

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    Book Chapter

    Pages 71-76

    Periodic Orbits

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    Book Chapter

    Pages 77-86

    Vector Fields Possessing an Integral

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    Book Chapter

    Pages 87-89

    Index Theory

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    Book Chapter

    Pages 90-103

    Some General Properties of Vector Fields: Existence, Uniqueness, Differentiability, and Flows

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    Book Chapter

    Pages 104-116

    Asymptotic Behavior

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    Book Chapter

    Pages 117-121

    The Poincaré-Bendixson Theorem

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    Book Chapter

    Pages 122-150

    Poincaré Maps

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    Book Chapter

    Pages 151-156

    Conjugacies of Maps, and Varying the Cross-Section

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    Book Chapter

    Pages 157-168

    Structural Stability, Genericity, and Transversality

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    Book Chapter

    Pages 169-196

    Lagrange’s Equations

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    Book Chapter

    Pages 197-230

    Hamiltonian Vector Fields

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    Book Chapter

    Pages 231-233

    Gradient Vector Fields

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    Book Chapter

    Pages 234-241

    Reversible Dynamical Systems

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    Book Chapter

    Pages 242-244

    Asymptotically Autonomous Vector Fields

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    Book Chapter

    Pages 245-269

    Center Manifolds

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    Book Chapter

    Pages 270-355

    Normal Forms

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