ABSTRACT:

Abstract: We obtain large deviation estimates for a large class of nonuniformly hyperbolic systems: namely those modelled by Young towers. In particular, if the correlations decay only at a polynomial rate 1/n^d (d>0), then we obtain the large deviation estimate 1/n^d. Moreover, we exhibit examples where this estimate is essentially optimal: the decay rate is no better than 1/n^e for all e>d. (In the case of exponential decay of correlations, we obtain the standard exponential large deviation estimates given by a rate function.) This is mainly joint work with Matthew Nicol.