图书信息
图书目录
常微分方程：定性理论（影印版）
暂无简介
作者：
Luis Barreira, Claudia Valls
定价：
135.00元
出版时间：
2021-03-02
ISBN：
978-7-04-055631-5
物料号：
55631-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
常微分方程
重点项目：
暂无
版面字数：
540.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
- 前辅文
- 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
- Chapter 1. Ordinary Differential Equations
- 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. Hölder 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
- Chapter 3. Stability and Lyapunov Functions
- 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. Poincaré–Bendixson Theory
- §7.1. Limit sets
- §7.2. The Poincaré–Bendixson theorem
- §7.3. Exercises
- Chapter 6. Index Theory
- 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
- Chapter 8. Bifurcations and Center Manifolds
- Bibliography
- Index
