Statistical properties of mostly contracting fast-slow partially hyperbolic systems

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