Introduction to Smooth Ergodic Theory

By Luís Barreira, Yakov Pesin. Graduate Studies in Mathematics, 2013

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Table of contents: The core of the theory: * Examples of hyperbolic dynamical systems * General theory of Lyapunov exponents * Lyapunov stability theory of nonautonomous equations * Elements of the nonuniform hyperbolicity theory * Cocycles over dynamical systems * The Multiplicative Ergodic Theorem * Local manifold theory * Absolute continuity of local manifolds * Ergodic properties of smooth hyperbolic measures * Geodesic flows on surfaces of nonpositive curvature Selected advanced topics: * Cone technics * Partially hyperbolic diffeomorphisms with nonzero exponents * More examples of dynamical systems with nonzero Lyapunov exponents * Anosov rigidity * C^1 pathological behavior: Pugh's example * Bibliography * Index

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

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