Entry times distribution for dynamical balls on metric spaces

TL;DR

This paper demonstrates that in certain dynamical systems with specific mixing properties, the entry and return times for Bowen balls follow an exponential distribution, including systems modeled by Young's tower.

Contribution

It establishes exponential distribution results for entry and return times of dynamical balls in systems with $\alpha$-mixing measures and Young's tower models.

Findings

Entry and return times are exponential for systems with $\alpha$-mixing invariant measures.

Systems modeled by Young's tower exhibit exponential hitting time distribution.

Results apply to dynamical balls (Bowen balls) in metric spaces.

Abstract

We show that the entry and return times for dynamic balls (Bowen balls) is exponential for systems that have an $\alpha$-mixing invariant measure with certain regularities. We also show that systems modeled by Young's tower has exponential hitting time distribution for dynamical balls