Contents

Preface vii

Part 1. The Core of the Theory

Chapter 1. Examples of Hyperbolic Dynamical Systems 3

§1.1. Anosov diffeomorphisms 4

§1.2. Anosov flows 8

§1.3. The Katok map of the 2-torus 13

§1.4. Diffeomorphisms with nonzero Lyapunov exponents on

surfaces 23

§1.5. A flow with nonzero Lyapunov exponents 27

Chapter 2. General Theory of Lyapunov Exponents 33

§2.1. Lyapunov exponents and their basic properties 33

§2.2. The Lyapunov and Perron regularity coeﬃcients 38

§2.3. Lyapunov exponents for linear differential equations 41

§2.4. Forward and backward regularity. The Lyapunov–Perron

regularity 51

§2.5. Lyapunov exponents for sequences of matrices 56

Chapter 3. Lyapunov Stability Theory of Nonautonomous Equations 61

§3.1. Stability of solutions of ordinary differential equations 62

§3.2. Lyapunov absolute stability theorem 68

§3.3. Lyapunov conditional stability theorem 72

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