Fast-slow partially hyperbolic systems: beyond averaging. Part II (Statistical Properties)

Jacopo De Simoi, Carlangelo Liverani

Published 2014-08-23Version 1

We consider a class of $\mathcal C^{4}$ partially hyperbolic systems on $\mathbb T^2$ given by $\varepsilon$-perturbations of maps $F(x,\theta)=(f(x,\theta),\theta)$ where $f(\cdot,\theta)$ are $\mathcal C^{4}$ expanding maps of the circle. For sufficiently small $\varepsilon$ and an open set of perturbations we prove existence and uniqueness of a SRB measure and exponential decay of correlation for H\"older observables with explicit bounds on the decay rate.