Hyperbolic Flows

  • Luís Barreira
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In this chapter we recall in a pragmatic manner all the necessary notions and results from hyperbolic dynamics, starting with the notion of a hyperbolic set for a flow. In particular, we consider the Markov systems constructed by Bowen and Ratner for a locally maximal hyperbolic set, and we describe how they can be used to associate a symbolic dynamics to the hyperbolic set. This allows one to see the restriction of any smooth flow to a hyperbolic set as a factor of a suspension flow over a topological Markov chain.

Keywords

Sectional Curvature Unstable Manifold Smooth Manifold Height Function Compact Riemannian Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 27.
    R. Bowen, Symbolic dynamics for hyperbolic flows, Am. J. Math. 95 (1973), 429–460. MathSciNetMATHCrossRefGoogle Scholar
  2. 90.
    M. Ratner, Markov partitions for Anosov flows on n-dimensional manifolds, Isr. J. Math. 15 (1973), 92–114. MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Luís Barreira
    • 1
  1. 1.Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal

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