图书信息
图书目录
动力系统与线性代数（影印版）
暂无简介
作者：
Fritz Colonius,Wolfgang Kliemann
定价：
135.00元
出版时间：
2022-02-28
ISBN：
978-7-04-057021-2
物料号：
57021-00
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：
代数学
重点项目：
暂无
版面字数：
500.000千字
开本：
特殊
全书页数：
暂无
装帧形式：
精装
- 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
- Chapter 1. Autonomous Linear Differential and Difference Equations
- 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
- Chapter 6. Lyapunov Exponents and Linear Skew Product Systems
- Bibliography
- Index
