Poisson Approximations and Convergence Rates for Hyperbolic Dynamical Systems

Abstract

We prove the asymptotic functional Poisson laws in the total variation norm and obtain estimates of the corresponding convergence rates for a large class of hyperbolic dynamical systems. These results generalize the ones obtained before in this area. Applications to intermittent solenoids, Axiom A systems, H\'enon attractors and to billiards, are also considered.