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    • 非线性动力系统和混沌应用导论(第2版)
      • 作者:(英)维金斯
      • 出版社:世界图书出版公司
      • ISBN:9787510058448
      • 出版日期:2013/03/01
      • 页数:843
    • 售价:50
  • 内容大纲

  • 作者介绍

  • 目录

    Series Preface
    Preface to the Second Edition
    Introduction
    1 Equilibrium Solutions,Stability,and Linearized Stability
      1.1 Equilibria of Vector Fields
      1.2 Stability of Trajectories
      1.2a Linearization
      1.3 Maps
      1.3a Definitions of Stability for Maps
      1.3b Stability of Fixed Points of Linear Maps
      1.3c Stability of Fixed Points of Maps via the Linear Approximation
      1.4 Some Terminology Associated with Fixed Points
      1.5 Application to the Unforced Duffing Oscillator
      1.6 Exercises
    2 Liapunov Functions
    3 Invariant Manifolds:Linear and Nonlinear Systems
    4 Periodic Orbits
    5 Vector Fields Possessing an Integral
    6 Index Theory
    7 Some General Properties of Vector Fields: Existence,Uniqueness,Differentiability,and Flows
    8 Asymptotic Behavior
    9 The Poinear6-Bendixson Theorem
    10 Poinear6 Maps
    11 Conjugacies of Maps,and Varying the Cross.Section
    12 Structural Stability,Genericity,and Transversality
    13 Lagrange's Equations
    14 Hamiltonian vector Fields
    15 Gradient vector Fields
    16 Reversible Dynamical Systems
    17 Asymptotically Autonomous Vector Fields
    18 Center Manifolds
    19 Normal Forms
    20 Bifurcation of Fixed Points of Vector Fields
    21 Bifurcations of Fixed Points of Maps
    23 The Smale Horseshoe
    24 Symbolic Dynamics
    25 The Conley-Moser Conditions,or“How to Prove That a Dynamical System is Chaotic”
    26 Dynamics Near Homoclinic Points ofTwo-Dimensional Maps
    27 Orbits Homoclinic to Hyperbolic Fixed Points in Three-Dimensional Autonomous V.ector Fields
    28 Melnikov's Method for Homoclinic Orbits in Two-Dimensional,Time-Periodic Vector Fields
    29 Liapunov Exponents
    30 Chaos and Strange Attractors
    31 Hyperbolic Invariant Sets:A Chaotic Saddle
    32 Long Period Sinks in Dissipative Systems and Elliptic Islands in Conservative Systems
    33 Global Bifurcations Arising from Local Codimension--Two Bifurcations
    34 Glossary of Frequently Used Terms
    Bibliography
    Index

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