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

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

2011-12-08

arxiv.org/abs/1112.1934v1

Mathematics

Dynamical Systems

14 pages

Scientific paper

We study a random map $T$ which consists of intermittent maps ${T_{k}}_{k=1}^{K}$ and probability distribution ${p_{k,\epsilon}(x)}_{k=1}^{K}$. We prove existence of a unique absolutely continuous invariant measure (ACIM) for the random map $T$. Moreover, we show that, as $\epsilon$ 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 $T_{1}$.

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