Large deviations for non-uniformly expanding maps

Details Large deviations for non-uniformly expanding maps Large deviations for non-uniformly expanding maps

2006-01-18

arxiv.org/abs/math/0601449v3

Journal of Statistical Physics, v. 125, p. 415-457, 2007

Mathematics

Dynamical Systems

33 pages, 1 figure. Improved introduction and comments

Scientific paper

10.1007/s10955-006-9183-y

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of points whose time averages stay away from the space average decays to zero exponentially fast with the number of iterates involved. As easy by-products we deduce escape rates from subsets of the basins of physical measures for these types of maps. The rates of decay are naturally related to the metric entropy and pressure function of the system with respect to a family of equilibrium states.

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