Dolgopyat, Dmitry; Nándori, Péter; Pène, Françoise Asymptotic expansion of correlation functions for Zd covers of hyperbolic flows. (English. French summary) Zbl 1510.37039 Ann. Inst. Henri Poincaré, Probab. Stat. 58, No. 2, 1244-1283 (2022).

Abstract

The authors give asymptotic expansions for t→∞ of the correlation functions of sufficiently regular observables for Z^d extensions of a suitable class of hyperbolic flows, in an abstract setup. The class under study includes the finite horizon periodic Lorentz gas in dimension 2 (i.e., a Sinai billiard) and geodesic flows on abelian covers of compact Riemannian manifolds with negative curvature.