Quantitative statistical stability and speed of convergence to equilibrium for partially hyperbolic skew products

Stefano Galatolo

Published 2017-02-20Version 1

We consider a general relation between fixed point stability of suitably perturbed transfer operators and convergence to equilibrium (a notion which is strictly related to decay of correlations). We apply this relation to deterministic perturbations of a class of partially hyperbolic skew products, whose behavior on the preserved fibers is dominated by the expansion of the base map. In particular we apply the results to power law mixing toral extensions. It turns out that in this case, the dependence of the physical measure on small deterministic perturbations, in a suitable anisotropic metric, is Holder with an exponent which is explicitly estimated. We show explicit examples in that class having actually Holder behavior and non differentiable dependence of the physical measure on perturbations.