Stability of statistical properties for piecewise hyperbolic maps.
Abstract. I will discuss the statistical properties of piecewise smooth dynamical systems by studying directly the action of the transfer operator on appropriate spaces of distributions. In the case of two-dimensional maps with uniformly bounded second derivative, we obtain a complete description of the SRB measures, their statistical properties and their stability with respect to a large class of perturbations, including deterministic and random perturbations, as well as holes. This is based on joint work with C. Liverani.