Smooth Ergodic Theory and Nonuniformly Hyperbolic Dynamics
نویسندگان
چکیده
Introduction 1 1. Lyapunov exponents of dynamical systems 3 2. Examples of systems with nonzero exponents 6 3. Lyapunov exponents associated with sequences of matrices 18 4. Cocycles and Lyapunov exponents 24 5. Regularity and Multiplicative Ergodic Theorem 31 6. Cocycles over smooth dynamical systems 46 7. Methods for estimating exponents 54 8. Local manifold theory 62 9. Global manifold theory 73 10. Absolute continuity 79 11. Smooth invariant measures 83 12. Metric entropy 95 13. Genericity of systems with nonzero exponents 102 14. SRB-measures 112 15. Hyperbolic measures I: topological properties 120 16. Hyperbolic measures II: entropy and dimension 127 17. Geodesic flows on manifolds without conjugate points 133 18. Dynamical systems with singularities: the conservative case 138 19. Hyperbolic attractors with singularities 142 Appendix A. Decay of correlations, by Omri Sarig 151 References 160 Index 170
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