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Decay of random correlation functions for unimodal maps
KTH, Superseded Departments, Mathematics.
2000 (English)In: Reports on mathematical physics, ISSN 0034-4877, E-ISSN 1879-0674, Vol. 46, no 2-Jan, 15-26 p.Article in journal (Refereed) Published
Abstract [en]

Since the pioneering results of Jakobson and subsequent work by Benedicks-Carleson and others, it is known that quadratic maps f(a) (x) = a - x(2) admit a unique absolutely continuous invariant measure for a positive measure set of parameters a. For topologically mixing f(a), Young and Keller-Nowicki independently proved exponential decay of correlation functions for this a.c.i.m. and smooth observables. We consider random compositions of small perturbations f + omega (t), with f = f(a) or another unimodal map satisfying certain nonuniform hyperbolicity axioms, and omega (t) chosen independently and identically in [-epsilon, epsilon]. Baladi-Viana showed exponential mixing of the associated Markov chain, i.e., averaging over all random itineraries. We obtain stretched exponential bounds for the random correlation functions of Lipschitz observables for the sample measure mu (omega), of almost every itinerary.

Place, publisher, year, edition, pages
2000. Vol. 46, no 2-Jan, 15-26 p.
Keyword [en]
random perturbations, hyperbolicity
Identifiers
URN: urn:nbn:se:kth:diva-20152ISI: 000165239600003OAI: oai:DiVA.org:kth-20152DiVA: diva2:338845
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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