Scaling Invariance in a Time-Dependent Elliptical Billiard

TL;DR

This paper investigates how introducing time-dependent boundary motion in an elliptical billiard affects its dynamical behavior, revealing unbounded energy growth despite the static system's integrability.

Contribution

It demonstrates that a time-dependent perturbation causes unlimited energy growth in an otherwise integrable elliptical billiard system.

Findings

Unbounded energy growth observed with moving boundary.

Scaling arguments describe average velocity behavior.

Static elliptical billiard is integrable, but not under perturbation.

Abstract

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although the static elliptical billiard is an integrable system, after to introduce time-dependent perturbation on the boundary the unlimited energy growth is observed. The behaviour of the average velocity is described using scaling arguments.