Prevalence of marginally unstable periodic orbits in chaotic billiards

TL;DR

This paper investigates the widespread presence and influence of marginally unstable periodic orbits in chaotic billiards, revealing their significant role in classical and quantum dynamics through experiments and analysis.

Contribution

It uncovers the prevalence of marginally unstable periodic orbits in chaotic billiards and demonstrates their impact on system dynamics, both classically and quantum mechanically.

Findings

Marginally unstable periodic orbits are common in chaotic billiards.

These orbits significantly influence the dynamics of perturbed billiards.

Microwave experiments confirm their impact in quantum regimes.

Abstract

The dynamics of chaotic billiards is significantly influenced by coexisting regions of regular motion. Here we investigate the prevalence of a different fundamental structure, which is formed by marginally unstable periodic orbits and stands apart from the regular regions. We show that these structures both {\it exist} and {\it strongly influence} the dynamics of locally perturbed billiards, which include a large class of widely studied systems. We demonstrate the impact of these structures in the quantum regime using microwave experiments in annular billiards.