Quantifying intermittency in the open drivebelt billiard

TL;DR

This paper investigates the intermittent chaotic behavior of a drivebelt billiard, revealing how multiple MUPO families influence escape dynamics and potential applications like microlasers.

Contribution

It provides the first exact leading order coefficient for survival probability in a drivebelt billiard and highlights the effects of multiple MUPO families on intermittency.

Findings

Survival probability decays algebraically for fixed hole size.

In the small hole limit, decay remains exponential.

Multiple MUPO families lead to new dynamical effects.

Abstract

A "drivebelt" stadium billiard with boundary consisting of circular arcs of differing radius connected by their common tangents shares many properties with the conventional "straight" stadium, including hyperbolicity and mixing, as well as intermittency due to marginally unstable periodic orbits (MUPOs). Interestingly, the roles of the straight and curved sides are reversed. Here we discuss intermittent properties of the chaotic trajectories from the point of view of escape through a hole in the billiard, giving the exact leading order coefficient $\lim_{t\to\infty} t P(t)$ of the survival probability $P(t)$ which is algebraic for fixed hole size. However, in the natural scaling limit of small hole size inversely proportional to time, the decay remains exponential. The big distinction between the straight and drivebelt stadia is that in the drivebelt case there are multiple families of MUPOs leading to qualitatively new effects. A further difference is that most marginal periodic orbits in this system are oblique to the boundary, thus permitting applications that utilise total internal reflection such as microlasers.