Prevalence of marginally unstable periodic orbits in chaotic billiards
arXiv:0711.4585 · doi:10.1103/PhysRevE.77.016205
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.
arXiv comment6 pages, 5 figures
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- Linear and nonlinear stability of periodic orbits in annular billiards
- Chaotic properties of Coulomb-interacting circular billiards