《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 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
2.1 Exercises
3 Invariant Manifolds：Linear and Nonlinear Systems
3.1 Stable，Unstable，and Center Subspaces of Linear，Autonomous Vector Fields
3.1a Invariance of the Stable，Unstable，and Center Subspaces
3.1b Some Examples.
3.2 Stable，Unstable，and Center Manifolds for Fixed Points of Nonlinear，Autonomous Vector Fields
3.2a Invariance of the Graph of a Function：Tangency of the Vector Field to the Graph
3.3 Maps
3.4 Some Examples
3.5 Existence of Invariant Manifolds：The Main Methods of Proof,and HOW They Wbrk 3：5a Application of These Two Methods to a Concrete Example：Existence of the Unstable Manifold
3.6 Time-Dependent Hyperbolic Trajectories and their Stable and Unstable ManifoIds
3.6a Hyperbolic Trajectories
3.6b Stable and Unstable Manifolds of Hyperbolic Trajectories
3.7 Invariant Manifolds in a Broader Context
3.8 Exercises
4 Periodic Orbits
4.1 Nonexistence of Periodic Orbits for Two-Dimensional，Autonomous Vector Fields
4.2 Further Remarks on Periodic Orbits
4.3 Exercises
5 Vector Fields Possessing an Integral
5.1 Vector Fields on Two-Manifolds Having an Integral
5.2 Two Degree-of-Freedom Hamiltonian Systems and Geometry
5.2a Dynamics on the Energy Surface.
5.2b Dynamics on an Individual Torus
5.3 Exercises
6 Index Theory
6.1 Exercises
7 Some General Properties of Vector Fields：
Existence，Uniqueness，Differentiability,and Flows
7.1 Existence，Uniqueness，Differentiability with Respect to Initial Conditions
7.2 Continuation of Solutions
7.3 Differentiability with Respect to Parameters
7.4 Autonomous Vector Fields
7.5 Nonautonomous Vector Fields
7.5a The Skew—Product Flow Approach
7.5b The Cocycle Approach
7.5c Dynamics Generated by a Bi—Infinite Sequence of Maps
7.6 Liouville's Theorem
7.6a Volume Preserving Vector Fields and the Poincar6 Recurrence Theorem
7.7 Exercises
8 Asymptotic Behavior
8.1The Asymptotic Behavior ofTrajectories.
8.2 Attracting Sets，Attractors.and Basins of Attraction
8.3 The LaSalle Invariance Principle
8.4 Attraction in Nonautonomous Systems
8.5 Exercises
9 The Poinear6-Bendixson Theorem
9.1 Exercises
10 Poinear6 Maps
10.1 Cuse 1：Poincar6 Map Near a Periodic Orbit
10.2 Case 2：The Poincar6 Map of a Time-Periodic Ordinary Differential Equation
10.2a Periodically Forced Linear Oscillators
10.3 Case 3：The Poincar6 MaD Near a Homoclinic Orbit
10.4 Case 4：Poincar6 Map Associated with a Two Degree-of-Freedom Hamiltonian System
10.4a The Study of Coupled Oscillators via Circle Maps
10.5 Exercises