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Prevalence of marginally unstable periodic orbits in chaotic billiards

2007/11/28 by E. G. Altmann, Eduardo G. Altmann, T. Friedrich +6
Physics and Astronomy · #Chaos control and synchronization #Quantum chaos and dynamical systems #Scientific Research and Discoveries #nlin.CD #quant-ph

paper · pdf · doi:10.1103/physreve.77.016205

published as Phys. Rev. E 77, 016205 (2008) · 6 pages, 5 figures

arxiv created 2007/11/28 · openalex publication_date 2008/01/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 exist and 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.

Citations