Lectures on Lyapunov Exponents and Smooth Ergodic Theory
نویسنده
چکیده
1. Lyapunov Exponents for Differential Equations 2. Abstract Theory of Lyapunov Exponents 3. Regularity of Lyapunov Exponents Associated with Differential Equations 4. Lyapunov Stability Theory 5. The Oseledets Decomposition 6. Dynamical Systems with Nonzero Lyapunov Exponents. Multiplicative Ergodic Theorem 7. Nonuniform Hyperbolicity. Regular Sets 8. Examples of Nonuniformly Hyperbolic Systems 9. Existence of Local Stable Manifolds 10. Basic Properties of Local Stable and Unstable Manifolds 11. Absolute Continuity. Holonomy Map 12. Absolute Continuity and Smooth Invariant Measures 13. Ergodicity of Nonuniformly Hyperbolic Systems Preserving Smooth Measures 14. Local Ergodicity 15. The Entropy Formula 16. Ergodic Properties of Geodesic Flows on Compact Surfaces of Nonpositive Curvature
منابع مشابه
Lyapunov Exponents and Smooth Ergodic Theory
This book provides a systematic introduction to smooth ergodic theory, including the general theory of Lyapunov exponents, nonuniform hyperbolic theory, stable manifold theory emphasizing absolute continuity of invariant foliations, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. The book can be used as a primary textbook for a special topics course on nonuniform hy...
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