A recurrence-type strong Borel-Cantelli lemma for Axiom A diffeomorphisms
Let (X, μ, T , d) be a metric measure-preserving dynamical system such that three-fold correlations decay exponentially for Lipschitz continuous observables. Given a sequence (Mk) that converges to 0 slowly enough, we obtain a strong dynamical Borel.Cantelli result for recurrence, that is, for μ-almost every x ∈ X, {equation presented} where μ(Bk(x)) = Mk. In particular, we show that this result h