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, Λ is a mixing (or transitive) hyperbolic set, and V is a neighborhood of Λ, then there exists a mixing (or transitive) hyperbolic set Λ̃ with a Markov partition such that Λ Λ̃ V . We also show that in the topologically mixing case the set Λ̃ 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