slides

# Equilibrium States for Partially Hyperbolic Horseshoes

## Abstract

In this paper, we study ergodic features of invariant measures for the partially hyperbolic horseshoe at the boundary of uniformly hyperbolic diffeomorphisms constructed in \cite{DHRS07}. Despite the fact that the non-wandering set is a horseshoe, it contains intervals. We prove that every recurrent point has non-zero Lyapunov exponents and all ergodic invariant measures are hyperbolic. As a consequence, we obtain the existence of equilibrium measures for any continuous potential. We also obtain an example of a family of $C^\infty$ potentials with phase transition

## Full text

arXiv.org e-Print ArchiveProvided a free PDF (195.62 KB)

0801.1027oai:arXiv.org:0801.1027
Last time updated on April 13, 2012View original full text link

This paper was published in arXiv.org e-Print Archive.

# Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.