**Data:** 24/10/2018 - Quarta-feira**Horário:** 13:00**Local:** IM-UFRJ, CT

**Título:** A relative Ruelle-Peron-Frobenius theorem for random non-uniformly expanding maps

**Palestrante:** Shintaro Suzuki (UFBA)

**Resumo:** We consider a random dynamical system generated by non-uniformly expanding maps on a compact connected Riemannian manifold, which have contractive and expanding behavior on the manifold. For such a random dynamical system, under some suitable "mean expanding" condition, we prove a version of the Ruelle-Peron-Frobenius theorem for random transfer operators in the case where the associated potentials are C1 on each fiber and the mean oscillation of the potentials is sufficiently small. Our proof here is based on Birkhoff cone methods for random dynamical systems and we have fiberwise exponential decay of correlation functions as its application (joint work with M. Stadlbauer and P. Varandas ).