CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY

Abstract

CONTENTS Part I § 1. Introduction § 2. Prerequisites from ergodic theory § 3. Basic properties of the characteristic exponents of dynamical systems § 4. Properties of local stable manifolds Part II § 5. The entropy of smooth dynamical systems § 6. "Measurable foliations". Description of the π-partition § 7. Ergodicity of a diffeomorphism with non-zero exponents on a set of positive measure. The K-property § 8. The Bernoullian property § 9. Flows § 10. Geodesic flows on closed Riemannian manifolds without focal points References