Expositor: Bruno Santiago (UFF, Niteroi, Brasil). ht
Title: Approximation of ergodic invariant measures by horseshoes in the partially hyperbolic scenario
Abstract: A classical result of (uniformly) hyperbolic theory, due to Sigmund, asserts that the Dirac measures along periodic orbits are dense in the space of invariant measures and one can obtain, as consequence, that for topologically mixing basic pieces, the Bernoulli measures are also dense, showing the richness of this space. Latter developments showed that some "local" source of hyperbolicity suffices to these approximation results, like for C1 generic diffeomorphisms and non-uniformly hyperbolic diffeomorphisms. Therefore, the question we address is the following: can we reproduce these ergodic approximations in the partially hyperbolic context? In this talk we will discuss how to use Blenders and minimality of both strong foliations to approach ergodic measures by uniformly hyperbolic horseshoes whose entropy and Lyapunov exponent resembles those of the given measure. This is a joint work with Lorenzo Diaz and Katrin Gelfert.