Contraction properties for random dynamical systems

Graccyela Salcedo (ICMC-USP)

We study contraction properties for Random Dynamical Systems (RDS) on a compact metric space (M, d). Specifi- cally, we study local contraction (LC) and contraction on average (CA) for RDS. We establish that the LC property has several consequences. In particular, we show that under LC property a RDS is CA (with respect to a metric equivalent to d) if and only if it has only one stationary measure. We also establish interesting probabilistic theorems for Markov chains generated by a RDS. This is a joint work with Katrin Gelfert.