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常微分方程:定性理论(影印版)


作者:
Luis Barreira, Claudia Valls
定价:
135.00元
ISBN:
978-7-04-055631-5
版面字数:
540.000千字
开本:
16开
全书页数:
暂无
装帧形式:
精装
重点项目:
暂无
出版时间:
2021-03-02
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
  • 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. 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
  • 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
  • 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

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