Asymptotic expansion of correlation functions for ${\mathbb{Z}}^d$ covers of hyperbolic flows

Abstract

We establish expansion of every order for the correlation function of sufficiently regular observables of ${\mathbb{Z}}^d$ extensions of some hyperbolic flows. Our examples include the ${\mathbb{Z}}^2$ periodic Lorentz gas and geodesic flows on abelian covers of compact manifolds with negative curvature.