Journal of Statistical Physics

, Volume 125, Issue 2, pp 411–453 | Cite as

Large Deviations for Non-Uniformly Expanding Maps

  • V. AraújoEmail author
  • M. J. Pacifico


We obtain large deviation bounds 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 tends 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.


non-uniform expansion physical measures hyperbolic times large deviations 


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© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil
  2. 2.Centro de Matemática da Universidade do PortoPortoPortugal

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