Robustly chain transitive diffeomorphisms

Unique Equilibrium States for the Robustly Transitive Diffeomorphisms of Mañé and Bonatti–viana

We show that the families of robustly transitive diffeomorphisms of Mañé and Bonatti–Viana have unique equilibrium states for natural classes of potentials. In particular, for any Hölder continuous potential on the phase space of one of these families, we construct a C-open neighborhood of a diffeomorphism in that family for which the potential has a unique equilibrium state. We also characteri...

Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds

Contribution to the Ergodic Theory of Robustly Transitive Maps

In this article we intend to contribute in the understanding of the ergodic properties of the set RT of robustly transitive local diffeomorphisms on a compact manifold M without boundary. We prove that there exists a C residual subset R0 ⊂ RT such that any f ∈ R0 has a residual subset of M with dense pre-orbits. Moreover, C generically in the space of robustly transitive local diffeomorphisms w...

Intrinsic Ergodicity for Certain Nonhyperbolic Robustly Transitive Systems

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 constant entropy and isomorphic unique measures of maximal entropy.

C-robust Transitivity for Surfaces with Boundary

We prove that C-robustly transitive diffeomorphisms on surfaces with boundary do not exist, and we exhibit a class of diffeomorphisms of surfaces with boundary which are C−robustly transitive, with k ≥ 2. This class of diffeomorphisms are examples where a version of Palis’ conjecture on surfaces with boundary, about homoclinic tangencies and uniform hyperbolicity, does not hold in the C−topolog...