本书讨论了线性代数与连续、离散动力系统的相互作用。书中首先回顾了矩阵A在R^d中和Grassmann流形上的诱导动力系统的自治情形；然后给出了主要的非自治方法，其中A(t)的时间依赖性是通过斜积流的周期性、拓扑性（链递归）或遍历性（不变测度）给出的。作者推广了特征值（的实部）和特征空间作为时变线性系统——周期、随机和摄动（或受控）系统——的线性代数的起点。 本书首次在一本书中，通过Lyapunov指数详细证明了Floquet理论、Morse谱的性质以及随机矩阵乘积的乘法遍历理论。作者对链递归、Morse分解以及经典遍历理论等主要工具的讲解清晰、透彻，刚入学的研究生就可以理解和掌握。

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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