We characterize two of the most studied non-uniform hyperbolicity conditions for rational maps, semi-hyperbolicity and the topological Collet-Eckmann condition, in terms of the maximal entropy measure.

We consider a wide family of non-uniformly expanding maps and hyperbolic Hölder continuous potentials. We prove that the unique equilibrium state associated to each element of this family is given by the eigenfunction of ...

Usamos o Princípio de Invariância de Ávila e Viana para provar que todo difeomorfismo simplético parcialmente hiperbólico com feixe central bidimensional, tendo um ponto periódico e satisfazendo certas condições de pinçamento ...

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise ...

We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding ...

We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding ...

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise ...

We prove that, under a mild condition on the hyperbolicity of its periodic points, a map g which is topologically conjugated to a hyperbolic map (respectively, an expanding map) is also a hyperbolic map (respectively, an ...