Equilibrium States for Partially Hyperbolic Horseshoes

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dc.creatorLeplaideur, Renaud
dc.creatorOliveira, Krerley
dc.creatorRios, Isabel
dc.date2008-01-07
dc.date.accessioned2026-07-07T08:53:00Z
dc.date.available2026-07-07T08:53:00Z
dc.descriptionIn 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.
dc.identifierhttps://arxiv.org/abs/0801.1027
dc.identifierhttp://arxiv.org/abs/0801.1027
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145471
dc.subjectDynamical Systems
dc.titleEquilibrium States for Partially Hyperbolic Horseshoes
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