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Statistical properties of mostly contracting fast-slow partially hyperbolic systems

Research paper by Jacopo De Simoi, Carlangelo Liverani

Indexed on: 15 Oct '15Published on: 15 Oct '15Published in: Mathematics - Dynamical Systems



Abstract

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