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.