Asymptotic measures of random logistic maps

Abstract

In this paper, we consider a system whose state x changes to F-sigma(x) if a perturbation occurs at the time t, for t > 0

t is not an element of N and the state x changes to the new state F-eta(x) at the time t, for t is an element of N. Here, F-eta and F-sigma are logistic maps. We assume that the number of perturbations in the interval (n

n + 1) is a discrete random variable c(n). We show that under certain conditions on the parameters eta and sigma, 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.