Description

Book Synopsis
Provides the first comprehensive introduction to smooth ergodic theory. The book first introduces the core of the theory and then discusses more advanced topics. It includes more than 80 exercises.

Table of Contents
  • The core of the theory: Examples of hyperbolic dynamical systems
  • General theory of Lyapunov exponents
  • Cocylces over dynamical systems
  • The multiplicative ergodic theorem
  • Elements of the nonuniform hyperbolicity theory
  • Lyapunov stability theory of nonautonomous equations
  • Local manifold theory
  • Absolute continuity of local manifolds
  • Ergodic properties of smooth hyperbolic measures
  • Geodesic flows on surfaces of nonpositive curvature
  • Topological and ergodic properties of hyperbolic measures
  • Selected advanced topics: Cone techniques
  • 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

Introduction to Smooth Ergodic Theory

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    A Hardback by Luis Barreira, Yakov Pesin

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      Book details

      Publisher American Mathematical Society
      Published 8 September 2023
      ISBN-13 9781470470654
      978-1470470654
      ISBN-10 1470470659

      Description

      Book Synopsis
      Provides the first comprehensive introduction to smooth ergodic theory. The book first introduces the core of the theory and then discusses more advanced topics. It includes more than 80 exercises.

      Table of Contents
      • The core of the theory: Examples of hyperbolic dynamical systems
      • General theory of Lyapunov exponents
      • Cocylces over dynamical systems
      • The multiplicative ergodic theorem
      • Elements of the nonuniform hyperbolicity theory
      • Lyapunov stability theory of nonautonomous equations
      • Local manifold theory
      • Absolute continuity of local manifolds
      • Ergodic properties of smooth hyperbolic measures
      • Geodesic flows on surfaces of nonpositive curvature
      • Topological and ergodic properties of hyperbolic measures
      • Selected advanced topics: Cone techniques
      • 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

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