Trans. Amer. Math. Soc. 360 (2008) 6661-6676.
Ian Melbourne and Matthew Nicol
Abstract
We obtain large deviation estimates for a large class of nonuniformly hyperbolic systems: namely those modelled by Young towers with summable decay of correlations. In the case of exponential decay of correlations, we obtain exponential large deviation estimates given by a rate function. In the case of polynomial decay of correlations, we obtain polynomial large deviation estimates, and exhibit examples where these estimates are essentially optimal.
In contrast with many treatments of large deviations, our methods do not
rely on thermodynamic formalism. Hence, for Hölder observables we are
able to obtain
exponential estimates in situations where the
space of equilibrium measures is not known to be a singleton, as well
as polynomial estimates in situations where there is not a unique
equilibrium measure.