Hyperbolic Flows

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


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.


Sectional Curvature Unstable Manifold Smooth Manifold Height Function Compact Riemannian Manifold 
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  1. 27.
    R. Bowen, Symbolic dynamics for hyperbolic flows, Am. J. Math. 95 (1973), 429–460. MathSciNetzbMATHCrossRefGoogle Scholar
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    M. Ratner, Markov partitions for Anosov flows on n-dimensional manifolds, Isr. J. Math. 15 (1973), 92–114. MathSciNetzbMATHCrossRefGoogle 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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