TY - JOUR

T1 - Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems

AU - Buzzi, J.

AU - Fisher, T.

AU - Sambarino, M.

AU - Vásquez, C.

PY - 2012/2

Y1 - 2012/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84555169038&partnerID=8YFLogxK

U2 - 10.1017/S0143385710000854

DO - 10.1017/S0143385710000854

M3 - Article

AN - SCOPUS:84555169038

SN - 0143-3857

VL - 32

SP - 63

EP - 79

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 1

ER -