POISSON LAW FOR AXIOM-A DIFFEOMORPHISMS

Let f be an Axiom A diffeomorphism, OMEGA its non wandering set, mu the Gibbs measure for the Lipschitz continuous potential. We consider the (suitably normalized) return times of the orbit to the epsilon-neighborhood of a point z is-an-element-of OMEGA and prove that for mu-a.e. z the sequence of the normalized return times converges to the Poisson point process in finite dimensional distribution as epsilon --> 0.