Recurrence of particles in static and time varying oval billiards

TL;DR

This paper investigates how particles escape and recur in oval billiards with static and moving boundaries, revealing different decay behaviors in recurrence times and the influence of sticky orbits.

Contribution

It compares recurrence time distributions in static and periodically moving oval billiards, highlighting the effects of boundary motion on sticky orbits and escape dynamics.

Findings

Static billiards show exponential, power law, or stretched exponential decay in recurrence times.

Moving boundaries reduce the prominence of sticky orbits.

Sticky orbits are less evident in time-dependent billiards.

Abstract

Dynamical properties are studied for escaping particles, injected through a hole in an oval billiard. The dynamics is considered for both static and periodically moving boundaries. For the static boundary, two different decays for the recurrence time distribution were observed after exponential decay for short times: A changeover to: (i) power law or; (ii) stretched exponential. Both slower decays are due to sticky orbits trapped near KAM islands, with the stretched exponential apparently associated with a single group of large islands. For time dependent case, survival probability leads to the conclusion that sticky orbits are less evident compared with the static case.