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Introduction to Smooth Ergodic Theory

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Table of Contents

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

About the Author

Luis Barreira, Instituto Superior Tecnico, Lisbon, Portugal.

Yakov Pesin, Pennsylvania State University, State College, PA, USA.

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