图书信息
图书目录
常微分方程与动力系统（影印版）
暂无简介
作者：
Gerald Teschl
定价：
169.00元
出版时间：
2021-03-22
ISBN：
978-7-04-055648-3
物料号：
55648-00
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：
630.000千字
开本：
特殊
全书页数：
暂无
装帧形式：
精装
- 前辅文
- Part 1. Classical theory
- Chapter 1. Introduction
- §1.1. Newton’s equations
- §1.2. Classification of differential equations
- §1.3. First-order autonomous equations
- §1.4. Finding explicit solutions
- §1.5. Qualitative analysis of first-order equations
- §1.6. Qualitative analysis of first-order periodic equations
- Chapter 2. Initial value problems
- §2.1. Fixed point theorems
- §2.2. The basic existence and uniqueness result
- §2.3. Some extensions
- §2.4. Dependence on the initial condition
- §2.5. Regular perturbation theory
- §2.6. Extensibility of solutions
- §2.7. Euler’s method and the Peano theorem
- Chapter 3. Linear equations
- §3.1. The matrix exponential
- §3.2. Linear autonomous first-order systems
- §3.3. Linear autonomous equations of order n
- §3.4. General linear first-order systems
- §3.5. Linear equations of order n
- §3.6. Periodic linear systems
- §3.7. Perturbed linear first-order systems
- §3.8. Appendix: Jordan canonical form
- Chapter 4. Differential equations in the complex domain
- §4.1. The basic existence and uniqueness result
- §4.2. The Frobenius method for second-order equations
- §4.3. Linear systems with singularities
- §4.4. The Frobenius method
- Chapter 5. Boundary value problems
- §5.1. Introduction
- §5.2. Compact symmetric operators
- §5.3. Sturm–Liouville equations
- §5.4. Regular Sturm–Liouville problems
- §5.5. Oscillation theory
- §5.6. Periodic Sturm–Liouville equations
- Chapter 1. Introduction
- Part 2. Dynamical systems
- Chapter 6. Dynamical systems
- §6.1. Dynamical systems
- §6.2. The flow of an autonomous equation
- §6.3. Orbits and invariant sets
- §6.4. The Poincar´e map
- §6.5. Stability of fixed points
- §6.6. Stability via Liapunov’s method
- §6.7. Newton’s equation in one dimension
- Chapter 7. Planar dynamical systems
- §7.1. Examples from ecology
- §7.2. Examples from electrical engineering
- §7.3. The Poincar´e–Bendixson theorem
- Chapter 8. Higher dimensional dynamical systems
- §8.1. Attracting sets
- §8.2. The Lorenz equation
- §8.3. Hamiltonian mechanics
- §8.4. Completely integrable Hamiltonian systems
- §8.5. The Kepler problem
- §8.6. The KAM theorem
- Chapter 9. Local behavior near fixed points
- §9.1. Stability of linear systems
- §9.2. Stable and unstable manifolds
- §9.3. The Hartman–Grobman theorem
- §9.4. Appendix: Integral equations
- Chapter 6. Dynamical systems
- Part 3. Chaos
- Chapter 10. Discrete dynamical systems
- §10.1. The logistic equation
- §10.2. Fixed and periodic points
- §10.3. Linear difference equations
- §10.4. Local behavior near fixed points
- Chapter 11. Discrete dynamical systems in one dimension
- §11.1. Period doubling
- §11.2. Sarkovskii’s theorem
- §11.3. On the definition of chaos
- §11.4. Cantor sets and the tent map
- §11.5. Symbolic dynamics
- §11.6. Strange attractors/repellers and fractal sets
- §11.7. Homoclinic orbits as source for chaos
- Chapter 12. Periodic solutions
- §12.1. Stability of periodic solutions
- §12.2. The Poincar´e map
- §12.3. Stable and unstable manifolds
- §12.4. Melnikov’s method for autonomous perturbations
- §12.5. Melnikov’s method for nonautonomous perturbations
- Chapter 13. Chaos in higher dimensional systems
- §13.1. The Smale horseshoe
- §13.2. The Smale–Birkhoff homoclinic theorem
- §13.3. Melnikov’s method for homoclinic orbits
- Chapter 10. Discrete dynamical systems
- Bibliographical notes
- Bibliography
- Glossary of notation
- Index
