Decay of correlations and laws of rare events for random maps with a dense orbit

Vitor Araujo, Hale Aytaç

Published 2016-10-19Version 1

We show that uniformly continuous random perturbations of maps with a dense orbit define an aperiodic Harris chain which also satisfies Doeblin's condition. As a result, we get exponential decay of correlations for suitable random perturbations of such systems. We also prove that, for maps with a forward dense orbit, the limiting distribution for Extreme Value Laws (EVLs) and Hitting/Return Time Statistics (HTS/RTS) is standard exponential. Moreover, we show that the Rare Event Point Process (REPP) converges in distribution to a standard Poisson process.