Poisson Approximations and Convergence Rates for Hyperbolic Dynamical Systems

TL;DR

This paper establishes Poisson law approximations and convergence rates for a broad class of hyperbolic dynamical systems, extending previous results and applying to various complex systems like billiards and attractors.

Contribution

It generalizes existing Poisson approximation results to a wider class of hyperbolic systems with explicit convergence rate estimates.

Findings

Proves asymptotic Poisson laws in total variation norm

Provides convergence rate estimates for hyperbolic systems

Applies results to billiards, attractors, and intermittent 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.