A.C.I.M for Random Intermittent Maps : Existence, Uniqueness and Stochastic Stability

Abstract: We study a random map $T$ which consists of intermittent maps ${T_{k}}{k=1}^{K}$ and a position dependent probability distribution ${p{k,\varepsilon}(x)}{k=1}^{K}$. We prove existence of a unique absolutely continuous invariant measure (ACIM) for the random map $T$. Moreover, we show that, as $\varepsilon$ 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 $T{1}$. The outcome of this paper contains a first result on stochastic stability, in the strong sense, of intermittent maps.