Abstract: Our setting is partially hyperbolic and we consider diffeomorphisms whose splittings have a one-dimensional center having simultaneously ergodic measures with positive and negative center Lyapunov exponent. The goal is to understand the structure of the space of invariant measures.
After briefly discussing robust heterodimensional cycles of diffeomorphisms, we will discuss the notion of a cycle of an ergodic measure and its impact in the structure of ergodic measures. We will outline some consequences and provide some examples.
This is a join work with C. Bonatti (Univ. Burgundy, France) and K. Gelfert (UFRJ, Brazil).
