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

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