Decay of correlations for slowly mixing flows

Abstract

We show that polynomial decay of correlations is prevalent for a class of nonuniformly hyperbolic flows. These flows are the continuous time analogue of a class of nonuniformly hyperbolic diffeomorphisms for which Young proved polynomial decay of correlations. Roughly speaking, in situations where the decay rate $O(1/n^{\beta })$ has previously been proved for diffeomorphisms, we establish the decay rate $O(1/t^{\beta })$ for typical flows. Applications include certain classes of semidispersing billiards, as well as dispersing billiards with vanishing curvature. In addition, we obtain results for suspension flows with unbounded roof functions. This includes the planar periodic Lorentz flow with infinite horizon.

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