Lower Bounds for the Decay of Correlations in Non-uniformly Expanding Maps
Résumé
We give conditions under which nonuniformly expanding maps exhibit a lower bound of polynomial type for the decay of correlations and for a large class of observables. We show that if the Lasota-Yorke type inequalities for the transfer operator of a first return map are satisfied in a Banach space B, and the absolutely continuous invariant measure obtained is weak mixing, in terms of aperiodicity, then under some renewal condition, the maps has polynomial decay of correlations for observables in B. We also provide some general conditions that give aperiodicity for expanding maps in higher dimensional spaces. As applications, we obtain polynomial decay, including lower bound in some cases, for piecewise expanding maps with an indifferent fixed point and for which we also allow non-markov structure and unbounded distortion. The observables are functions that have bounded variation or satisfy quasi-Hölder conditions respectively and, in the case of polynomial lower bounds, they have the support avoiding the neutral fixed points.
Domaines
Systèmes dynamiques [math.DS]
Origine : Fichiers produits par l'(les) auteur(s)
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