Statistical properties of mostly contracting fast-slow partially hyperbolic systems

Abstract

We consider a class of ${\mathcal{C}}^4$ partially hyperbolic systems on ${\mathbb{T}}^2$ described by maps $F_{\epsilon }(x,\theta )=(f(x,\theta ),\theta +\epsilon \omega (x,\theta ))$ where $f(\cdot ,\theta )$ are expanding maps of the circle. For sufficiently small $\epsilon$ and $\omega$ generic in an open set, we precisely classify the SRB measures for $F_{\epsilon }$ and their statistical properties, including exponential decay of correlation for Hölder observables with explicit and nearly optimal bounds on the decay rate.

References in corpus (1)

• Geometric and measure-theoretical structures of maps with mostly contracting center

Cited by in corpus (1)

• On the smooth dependence of SRB measures for partially hyperbolic systems