Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds

Snir Ben Ovadia

doi:10.3934/jmd.2018013

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2018, Volume 13: 43-113. Doi: 10.3934/jmd.2018013

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Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds

Snir Ben Ovadia

Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, 234 Herzl Street, POB 26, Rehovot, 7610001 Israel

Received: April 23, 2017

Revised: October 27, 2018

Published: December 2018

This work is a part of a M.Sc. thesis at the Weizmann Institute of Science. The author was partly supported by the ISF grant 199/14.

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Abstract

We construct countable Markov partitions for non-uniformly hyperbolic diffeomorphisms on compact manifolds of any dimension, extending earlier work of Sarig [29] for surfaces. These partitions allow us to obtain symbolic coding on invariant sets of full measure for all hyperbolic measures whose Lyapunov exponents are bounded away from zero by a fixed constant. Applications include counting results for hyperbolic periodic orbits, and structure of hyperbolic measures of maximal entropy.

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Mathematics Subject Classification: Primary: 37D25; Secondary: 37B10.

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