Prevalence of marginally unstable periodic orbits in chaotic billiards

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.

6 pages, 5 figures

References in corpus (4)

• Stickiness in mushroom billiards
• Spectral properties of Bunimovich mushroom billiards
• Influence of classical resonances on chaotic tunnelling
• Nonperiodic echoes from mushroom billiard hats

Cited by in corpus (2)

• Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics
• Marginally Unstable Periodic Orbits in Semiclassical Mushroom Billiards