Fast-Slow Partially Hyperbolic Systems beyond Averaging
Jacopo De Simoi
Lots of attention and research activity has been devoted to partially
hyperbolic dynamical systems and their perturbations in the past few
decades; however, the main emphasis has been on features such as stable
ergodicity and accessibility rather than stronger statistical properties
such as existence of SRB measures and exponential decay of correlations. In
fact, these properties have been previously proved under some specific
conditions (e.g. Anosov flows, skew products) which, in particular, do not
persist under perturbations. In this talk, we will construct an open (and
thus stable for perturbations) class of partially hyperbolic smooth local
diffeomorphisms of the two-torus which admit a unique SRB measure
satisfying exponential decay of correlations for Hölder observables.
This is joint work with C. Liverani.