Stochastic stability for fiber expanding maps via a perturbative spectral approach (Q2810661)

The study of the spectral gap of the transfer operator for dynamical systems is the main tool to investigate some statistical properties, such as the existence of SRB measure, the exponential decay of correlations and the central limit theorem. These statistical properties and quantities are expected to be stable if the spectrum of the transfer operator is also stable. This perturbation spectral approach was initially applied to expanding maps, and then extended to skew-product mappings with mixing or invertible base dynamics.NEWLINENEWLINEIn this paper, the author extends this approach to skew-product mappings, in which the base dynamics are not necessarily mixing or invertible. The stochastic stability and upper bounds of the exponential decay of correlation of corresponding maps are demonstrated.