动力系统与线性代数（影印版）

样章

作者：

Fritz Colonius,Wolfgang Kliemann

定价：

135.00 元

版面字数：

500千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2022年

ISBN：

978-7-04-057021-2

物料号：

57021-00

出版时间：

2022-02-28

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：

代数学

暂无

目录
- 前辅文
- Part 1. Matrices and Linear Dynamical Systems
  - Chapter 1. Autonomous Linear Differential and Difference Equations
    - 1.1. Existence of Solutions
    - 1.2. The Real Jordan Form
    - 1.3. Solution Formulas
    - 1.4. Lyapunov Exponents
    - 1.5. The Discrete-Time Case: Linear Difference Equations
    - 1.6. Exercises
    - 1.7. Orientation, Notes and References
  - Chapter 2. Linear Dynamical Systems in Rd
    - 2.1. Continuous-Time Dynamical Systems or Flows
    - 2.2. Conjugacy of Linear Flows
    - 2.3. Linear Dynamical Systems in Discrete Time
    - 2.4. Exercises
    - 2.5. Orientation, Notes and References
  - Chapter 3. Chain Transitivity for Dynamical Systems
    - 3.1. Limit Sets and Chain Transitivity
    - 3.2. The Chain Recurrent Set
    - 3.3. The Discrete-Time Case
    - 3.4. Exercises
    - 3.5. Orientation, Notes and References
  - Chapter 4. Linear Systems in Projective Space
    - 4.1. Linear Flows Induced in Projective Space
    - 4.2. Linear Difference Equations in Projective Space
    - 4.3. Exercises
    - 4.4. Orientation, Notes and References
  - Chapter 5. Linear Systems on Grassmannians
    - 5.1. Some Notions and Results from Multilinear Algebra
    - 5.2. Linear Systems on Grassmannians and Volume Growth
    - 5.3. Exercises
    - 5.4. Orientation, Notes and References
- Part 2. Time-Varying Matrices and Linear Skew Product Systems
  - Chapter 6. Lyapunov Exponents and Linear Skew Product Systems
    - 6.1. Existence of Solutions and Continuous Dependence
    - 6.2. Lyapunov Exponents
    - 6.3. Linear Skew Product Flows
    - 6.4. The Discrete-Time Case
    - 6.5. Exercises
    - 6.6. Orientation, Notes and References
  - Chapter 7. Periodic Linear Differential and Difference Equations
    - 7.1. Floquet Theory for Linear Difference Equations
    - 7.2. Floquet Theory for Linear Differential Equations
    - 7.3. The Mathieu Equation
    - 7.4. Exercises
    - 7.5. Orientation, Notes and References
  - Chapter 8. Morse Decompositions of Dynamical Systems
    - 8.1. Morse Decompositions
    - 8.2. Attractors
    - 8.3. Morse Decompositions, Attractors, and Chain Transitivity
    - 8.4. Exercises
    - 8.5. Orientation, Notes and References
  - Chapter 9. Topological Linear Flows
    - 9.1. The Spectral Decomposition Theorem
    - 9.2. Selgrade’s Theorem
    - 9.3. The Morse Spectrum
    - 9.4. Lyapunov Exponents and the Morse Spectrum
    - 9.5. Application to Robust Linear Systems and Bilinear Control Systems
    - 9.6. Exercises
    - 9.7. Orientation, Notes and References
  - Chapter 10. Tools from Ergodic Theory
    - 10.1. Invariant Measures
    - 10.2. Birkhoff’s Ergodic Theorem
    - 10.3. Kingman’s Subadditive Ergodic Theorem
    - 10.4. Exercises
    - 10.5. Orientation, Notes and References
  - Chapter 11. Random Linear Dynamical Systems
    - 11.1. The Multiplicative Ergodic Theorem (MET)
    - 11.2. Some Background on Projections
    - 11.3. Singular Values, Exterior Powers, and the Goldsheid-Margulis Metric
    - 11.4. The Deterministic Multiplicative Ergodic Theorem
    - 11.5. The Furstenberg-Kesten Theorem and Proof of the MET in Discrete Time
    - 11.6. The Random Linear Oscillator
    - 11.7. Exercises
    - 11.8. Orientation, Notes and References
- Bibliography
- Index