本书全面介绍了常微分方程的定性理论，讨论了解的存在性和唯一性、相图、线性方程、稳定性理论、双曲性和平面方程。本书重点主要放在无需明确求解方程，即可分析解的定性性质的结果和方法上。书中包含许多例子，它们和每章末尾的习题详细阐明了新的概念和结果。本书还旨在成为通往一些重要主题的桥梁，这些主题通常在常微分方程课程中被遗漏。特别地，它简要介绍了分歧理论、中心流形、范式和Hamilton系统。

Preface
Part 1. Basic Concepts and Linear Equations
Chapter 1 Ordinary Differential Equations
1.1 Basic notions
1.2 Existence and uniqueness of solutions
1.3 Additional properties
1.4 Existence of solutions for continuous fields
1.5 Phase portraits
1.6 Equations on manifolds
1.7 Exercises
Chapter 2 Linear Equations and Conjugacies
2.1 Nonautonomous linear equations
2.2 Equations with constant coefficients
2.3 Variation of parameters formula
2.4 Equations with periodic coefficients
2.5 Conjugacies between linear equations
2.6 Exercises
Part 2. Stability and Hyperbolicity
Chapter 3 Stability and Lyapunov Functions
3.1 Notions of stability
3.2 Stability of linear equations
3.3 Stability under nonlinear perturbations
3.4 Lyapunov functions
3.5 Exercises
Chapter 4 Hyperbolicity and Topological Conjugacies
4.1 Hyperbolic critical points
4.2 The Grobman-Hartman theorem
4.3 HSlder conjugacies
4.4 Structural stability
4.5 Exercises
Chapter 5 Existence of Invariant Manifolds
5.1 Basic notions
5.2 The Hadamard-Perron theorem
5.3 Existence of Lipschitz invariant manifolds
5.4 Regularity of the invariant manifolds
5.5 Exercises
Part 3. Equations in the Plane
Chapter 6 Index Theory
6.1 Index for vector fields in the plane
6.2 Applications of the notion of index
6.3 Index of an isolated critical point
6.4 Exercises
Chapter 7 Poincar-Bendixson Theory
7.1 Limit sets
7.2 The Poincar6-Bendixson theorem
7.3 Exercises
Part 4. Further Topics
Chapter 8 Bifurcations and Center Manifolds
8.1 Introduction to bifurcation theory
8.2 Center manifolds and applications
8.3 Theory of normal forms
8.4 Exercises
Chapter 9 Hamiltonian Systems
9.1 Basic notions
9.2 Linear Hamiltonian systems
9.3 Stability of equilibria
9.4 Integrability and action-angle coordinates
9.5 The KAM theorem
9.6 Exercises
Bibliography
Index