Markov partitions for hyperbolic sets

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 $\tilde{\Lambda }$ with a Markov partition such that $\Lambda \subset \tilde{\Lambda }\subset V$. We also show that in the topologically mixing case the set $\tilde{\Lambda }$ will have a unique measure of maximal entropy.