Maximizing entropy measures for random dynamical systems

Abstract

We consider a class of endomorphisms which contains a set of piecewise partially hyperbolic skew-products with a non-uniformly expanding base map. The aimed transformation preserves a foliation which is almost everywhere uniformly contracted with possible disconti- nuity sets, which are parallel to the contracting direction. We prove that the associated transfer operator, acting on suitable anisotropic normed spaces, has a spectral gap (on which we have quantitative estimation) and the disintegration of the unique invariant physical measure, along the stable leaves, is ζ-Hölder. We use this fact to obtain exponential decay of correlations on the set of ζ-Hölder functions.

Rafael J. Álvarez

Professor