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常微分方程与动力系统（影印版）

样章
作者：
Gerald Teschl
定价：
169.00元
ISBN：
978-7-04-055648-3
版面字数：
630.000千字
开本：
特殊
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2021-03-22
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
暂无
  • 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
  • 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
  • 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
  • Bibliographical notes
  • Bibliography
  • Glossary of notation
  • Index

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