非線性動力系統和混沌應用導論 第二版 英文

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