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

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

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


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.

Original languageEnglish
Pages (from-to)63-79
Number of pages17
JournalErgodic Theory and Dynamical Systems
Issue number1
StatePublished - Feb 2012


Dive into the research topics of 'Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems'. Together they form a unique fingerprint.

Cite this