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 iii

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