Large Deviations for Non-Uniformly Expanding Maps

By Vitor Araujo, Maria José Pacifico. 2006

55 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/89331dbfe56c5f444c21fcc8b01f776d3590b05c

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In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Large deviations for nonuniformly hyperbolic systems (2008, background): “Again, the results in [1, 2] yield strong conclusions only when there is a unique equilibrium measure.”