Asymptotic measures of random logistic maps

Abstract

In this paper, we consider a system whose state x changes to if a perturbation occurs at the time t, for and the state x changes to the new state at the time t, for . Here, and are logistic maps. We assume that the number of perturbations in the interval is a discrete random variable . We show that under certain conditions on the parameters and , the system has, even for the non-contractive case, an unique stationary probability measure, the support of which can be either a Cantor set or an interval.