Asymptotic predictions using short-time data in oscillating billiards

TL;DR

This paper introduces a method to estimate the long-term energy growth rate in oscillating billiard systems using short-time data, revealing potential exponential growth in pseudo-integrable cases.

Contribution

It proposes a novel approach for predicting asymptotic energy growth rates from finite-time data in oscillating billiards, especially pseudo-integrable systems.

Findings

Energy growth in pseudo-integrable billiards can be exponential.

Short-time data can effectively estimate asymptotic growth rates.

The method bridges the gap between finite observations and long-term behavior.

Abstract

Particle motion in a smoothly oscillating non-integrable billiard is known to result in unbounded energy growth. Though the asymptotic energy growth rate of an ensemble of particles in an oscillating chaotic billiard is known to be quadratic, there are no estimates available for smoothly oscillating pseudo-integrable billiards. The energy growth rate in such systems is so slow that it is very hard to predict the asymptotic rates from finite time computations. In this paper, a method is proposed to estimate the asymptotic energy growth rate in a system by using short-time data. The idea is applied to the case of an oscillating pseudo-integrable system, and it is shown that the asymptotic energy growth rate in such systems could be exponential.