On statistical properties for equilibrium states of partially hyperbolic horseshoes

Abstract

We derive some statistical properties for equilibrium states of partially hyperbolic horseshoes. We define a projection map associated to the horseshoe and prove a spectral gap for its transfer operator acting on the space of Hölder continuous observables. From this we deduce an exponential decay of correlations and a central limit theorem. We finally extend these results to the horseshoe.

20 pages, 6 figures