Preprint D17/2006
Large deviations for non-uniformly expanding maps

Maria Jose Pacifico | Araujo, Vitor

**Keywords: **
non-uniform expansion | physical measures | hyperbolic times | large deviations

We obtain large deviation results 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 decays 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.