Statistical properties of random dynamical systems with contracting direction

Abstract

We present a mostly numerical investigation on randomly perturbed piecewise contracting maps (PCM) with the goal to study the extreme value limit distribution of observables related to local recurrence. Our analysis will focus on PCM under additive noise, but we will also consider the hyperbolic attractor of the Baker's map when perturbed with another kind of noise, namely, the randomly applied stochastic perturbation. A comparison of the two kind of noises will be considered with respect to the computation of the extremal index.