#### Vol. 2, No. 5, 2009

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Markov partitions for hyperbolic sets

### Todd Fisher and Himal Rathnakumara

Vol. 2 (2009), No. 5, 549–557
##### Abstract

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