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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
ISBN：
978-7-04-057021-2
版面字数：
500.000千字
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：
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
  • 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

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