Asymptotic expansion of correlation functions for \({\mathbb{Z}^d}\) covers of hyperbolic flows (Q2155536)

The authors give asymptotic expansions for \(t\to\infty\) of the correlation functions \(C_t(f,g)\) of sufficiently regular observables \(f,g\), for \(\mathbb{Z}^d\) extensions of a suitable class of hyperbolic flows, in an abstract setup. Such asymptotic expansions are of the form \[C_t(f,g)= \sum\limits_{p=0}^{P}C_p(f,g)t^{-\frac d2 - p} +o(t^{-\frac d2 - P}), \qquad P \in \mathbb{N},\] and 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.