Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems

Resumen

We show that a class of robustly transitive diffeomorphisms originally described by Mañé are intrinsically ergodic. More precisely, we obtain an open set of diffeomorphisms which fail to be uniformly hyperbolic and structurally stable, but nevertheless have the following stability with respect to their entropy. Their topological entropy is constant and they each have a unique measure of maximal entropy with respect to which periodic orbits are equidistributed. Moreover, equipped with their respective measure of maximal entropy, these diffeomorphisms are pairwise isomorphic. We show that the method applies to several classes of systems which are similarly derived from Anosov, i.e. produced by an isotopy from an Anosov system, namely, a mixed Mañé example and one obtained through a Hopf bifurcation.

Autores: Buzzi, J., Fisher, T., Sambarino, M., Vásquez, C.

Journal: Ergodic Theory and Dynamical Systems

Journal Volume: 32

Journal Issue: 1

Journal Page: 63-79

Tipo de publicación: ISI

Fecha de publicación: 2012

Topics:

DOI: 10.1017/S0143385710000854

URL de la publicación: https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/div-classtitlemaximal-entropy-measures-for-certain-partially-hyperbolic-derived-from-anosov-systemsdiv/EFDEC46EFA277CD97F51E6F7758CC3B1