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Abstract: We establish bounds for the measure of deviation sets associated tocontinuous observables with respect to not necessarily invariant weak Gibbsmeasures. Under some mild assumptions, we obtain upper and lower bounds for themeasure of deviation sets of some non-uniformly expanding maps, includingquadratic maps and robust multidimensional non-uniformly expanding localdiffeomorphisms. For that purpose, a measure theoretical weak form ofspecification is introduced and proved to hold for the robust classes ofmultidimensional nonuniformly expanding local diffeomorphisms and Viana maps.



Author: Paulo Varandas

Source: https://arxiv.org/



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