Non-uniform specification and large deviations for weak Gibbs measures

Details Non-uniform specification and large deviations for weak Gibbs measures Non-uniform specification and large deviations for weak Gibbs measures

2009-06-18

arxiv.org/abs/0906.3350v3

Mathematics

Dynamical Systems

30 pages, Final version

Scientific paper

We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of deviation sets of some non-uniformly expanding maps, including quadratic maps and robust multidimensional non-uniformly expanding local diffeomorphisms. For that purpose, a measure theoretical weak form of specification is introduced and proved to hold for the robust classes of multidimensional nonuniformly expanding local diffeomorphisms and Viana maps.

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