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Large deviations for nonuniformly hyperbolic systems

Melbourne, I and Nicol, M (2008) Large deviations for nonuniformly hyperbolic systems TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 360 (12). 6661 - 6676. ISSN 0002-9947

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Abstract

We obtain large deviation estimates for a large class of nonuniformly hyperbolic systems: namely those modelled by Young towers with summable decay of correlations. In the case of exponential decay of correlations, we obtain exponential large deviation estimates given by a rate function. In the case of polynomial decay of correlations, we obtain polynomial large deviation estimates, and exhibit examples where these estimates are essentially optimal. In contrast with many treatments of large deviations, our methods do not rely on thermodynamic formalism. Hence, for Holder observables we are able to obtain exponential estimates in situations where the space of equilibrium measures is not known to be a singleton, as well as polynomial estimates in situations where there is not a unique equilibrium measure.

Item Type: Article
Uncontrolled Keywords: Science & Technology, Physical Sciences, Mathematics, INDIFFERENT FIXED-POINTS, CENTRAL LIMIT-THEOREMS, DYNAMICAL-SYSTEMS, MIXING RATES, MAPS, BILLIARDS, DECAY, FLOWS, PRINCIPLES
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Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:40
Last Modified: 23 Sep 2013 18:32
URI: http://epubs.surrey.ac.uk/id/eprint/1370

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