Equilibrium States for Partially Hyperbolic Horseshoes
Dynamical Systems
2008-01-08 v1
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 potentials with phase transition.
Cite
@article{arxiv.0801.1027,
title = {Equilibrium States for Partially Hyperbolic Horseshoes},
author = {Renaud Leplaideur and Krerley Oliveira and Isabel Rios},
journal= {arXiv preprint arXiv:0801.1027},
year = {2008}
}