Almost sure rates of mixing for random intermittent maps

2018/01/29 by Ruziboev, Marks
#37A25 #37A50 37C40 37E05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.09583

Abstract

We consider a family \mathcal F of maps with two branches and a common neutral fixed point 0 such that the order of tangency at 0 belongs to some interval [α₀, α₁]⊂ (0, 1). Maps in \mathcal F do not necessarily share a common Markov partition. At each step a member of \mathcal F is chosen independently with respect to the uniform distribution on [α₀, α₁]. We show that the construction of the random tower in Bahsoun-Bose-Ruziboev \citeBBR with general return time can be carried out for random compositions of such maps. Thus their general results are applicable and gives upper bounds for the quenched decay of correlations of form n^1-1/α₀+δ for any δ>0.

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