1 research outputs found
Large deviations for non-uniformly expanding maps
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. 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. The corrections added to the published
version of this text appear in bold; see last section for a list of changesComment: 36 pages, 1 figure. After many PhD students and colleagues having
pointed several errors in the statements and proofs, this is a correction to
published article answering those comments. List of main changes in a new
last sectio