Meeting ID: 852 4277 3200 Passcode: 103121

For an iid IFS of continuous maps on the circle we discuss if and how a metric change can turn the system into one which contracts on average. In particular, we discuss the case of a system of C1 diffeomorphisms of maps which is proximal and does not preserve a common measure. In this case the IFS is exponentially synchronizing. We discuss how such techniques can be used to derive limit laws such as a quenched central limit theorem and we describe some large deviation results of synchronization rates and finite time Lyapunov exponents. This is joint work with Graccyela Salcedo (USP-São Carlos).