Markov partitions for hyperbolic sets

Fisher, Todd; Rathnakumara, Himal

doi:10.2140/involve.2009.2.549

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Markov partitions for hyperbolic sets

Todd Fisher and Himal Rathnakumara

Vol. 2 (2009), No. 5, 549–557

DOI: 10.2140/involve.2009.2.549

Abstract

We show that if $f$ is a diffeomorphism of a manifold to itself, $Λ$ is a mixing (or transitive) hyperbolic set, and $V$ is a neighborhood of $Λ$ , then there exists a mixing (or transitive) hyperbolic set $\tilde{Λ}$ with a Markov partition such that $Λ \subset \tilde{Λ} \subset V$ . We also show that in the topologically mixing case the set $\tilde{Λ}$ will have a unique measure of maximal entropy.

Keywords

Markov partitions, hyperbolic, entropy, specification, finitely presented

Mathematical Subject Classification 2000

Primary: 37A35, 37D05, 37D15

Milestones

Received: 13 January 2009

Revised: 1 September 2009

Accepted: 28 October 2009

Published: 13 January 2010

Communicated by Kenneth S. Berenhaut

Authors

Todd Fisher
Department of Mathematics Brigham Young University Provo, UT 84602 United States
http://math.byu.edu/~tfisher/
Himal Rathnakumara
Department of Mathematics Brigham Young University Provo, UT 84602 United States

Vol. 2, No. 5, 2009