Large Deviations for Non-Uniformly Expanding Maps |
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Authors: | V Araújo M J Pacifico |
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Institution: | (1) Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, 21.945-970 Rio de Janeiro, RJ, Brazil;(2) Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal |
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Abstract: | 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.
2000 Mathematics Subject Classification: 37D25, 37A50, 37B40, 37C40 |
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Keywords: | non-uniform expansion physical measures hyperbolic times large deviations |
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