维金斯编著的《非线性动力系统和混沌应用导论(第2版)(英文)》的重点讲述大量的技巧和观点，包括了深层次学习本科目的必备的核心知识，这些可以使学生能够学习特殊动力系统并获得学习这些系统大量信息。因此，像工程、物理、化学和生物专业读者不需要另外学习大量的预备知识。新的版本中包括了大量有关不变流形理论和规范模的新材料，拉格朗日、哈密尔顿、梯度和可逆动力系统的也有讨论，也包括了哈密尔顿分叉和环映射的基本性质。书中附了丰富的参考资料和详细的术语表，使得《非线性动力系统和混沌应用导论(第2版)(英文)》的可读性更加增大。

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