Journal of Statistical Physics

, Volume 146, Issue 2, pp 330–358 | Cite as

Non-uniform Specification and Large Deviations for Weak Gibbs Measures



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 non-uniformly expanding local diffeomorphisms and Viana maps.


Non-uniform specification Large deviations Hyperbolic times Weak Gibbs measure 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal da BahiaSalvadorBrazil

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