Contents Introduction xi Notation xv Part 1. Matrices and Linear Dynamical Systems Chapter 1. Autonomous Linear Differential and Difference Equations 3 §1.1. Existence of Solutions 3 §1.2. The Real Jordan Form 6 §1.3. Solution Formulas 10 §1.4. Lyapunov Exponents 12 §1.5. The Discrete-Time Case: Linear Difference Equations 18 §1.6. Exercises 24 §1.7. Orientation, Notes and References 27 Chapter 2. Linear Dynamical Systems in Rd 29 §2.1. Continuous-Time Dynamical Systems or Flows 29 §2.2. Conjugacy of Linear Flows 33 §2.3. Linear Dynamical Systems in Discrete Time 38 §2.4. Exercises 43 §2.5. Orientation, Notes and References 43 Chapter 3. Chain Transitivity for Dynamical Systems 47 §3.1. Limit Sets and Chain Transitivity 47 §3.2. The Chain Recurrent Set 54 vii
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