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.
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R. Bowen, Symbolic dynamics for hyperbolic flows, Am. J. Math. 95 (1973), 429–460.
M. Ratner, Markov partitions for Anosov flows on n-dimensional manifolds, Isr. J. Math. 15 (1973), 92–114.
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© 2013 Springer International Publishing Switzerland
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Barreira, L. (2013). Hyperbolic Flows. In: Dimension Theory of Hyperbolic Flows. Springer Monographs in Mathematics. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00548-5_3
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DOI: https://doi.org/10.1007/978-3-319-00548-5_3
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00547-8
Online ISBN: 978-3-319-00548-5
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