On mixing and the local central limit theorem for hyperbolic flows

Abstract

We formulate abstract conditions under which a suspension flow satisfies the local central limit theorem. We check the validity of these conditions for several systems including reward renewal processes, Axiom A flows, as well as the systems admitting Young’s tower, such as Sinai’s billiard with finite horizon, suspensions over Pomeau–Manneville maps, and geometric Lorenz attractors.