Exponential law for random maps on compact manifolds*

Abstract

Abstract We consider random dynamical systems on manifolds modelled by a skew product which have certain geometric properties and whose measures satisfy quenched decay of correlations at a sufficient rate. We prove that the limiting distribution for the hitting and return times to geometric balls are both exponential for almost every realisation. We then apply this result to random C 2 maps of the interval, random parabolic maps on the unit interval and random perturbation of partially hyperbolic attractors on a compact Riemannian manifold.