ACIM for random intermittent maps: existence, uniqueness and stochastic stability

摘要

We study a random map T which consists of intermittent maps {T_k}_k~k=1 and a position-dependent probability distribution {p_(k,ε)(x)}_k~K=1. We prove existence of a unique absolutely continuous invariant measure (ACIM) for the random map T. Moreover, we show that, as e goes to zero, the invariant density of the random system T converges in the L~1-norm to the invariant density of the deterministic intermittent map T. The outcome of this article contains a first result on stochastic stability, in the strong sense, of intermittent maps.