Coupling of bouncing-ball modes to the chaotic sea and their counting function
Chaotic Dynamics
2012-01-23 v2
Abstract
We study the coupling of bouncing-ball modes to chaotic modes in two-dimensional billiards with two parallel boundary segments. Analytically, we predict the corresponding decay rates using the fictitious integrable system approach. Agreement with numerically determined rates is found for the stadium and the cosine billiard. We use this result to predict the asymptotic behavior of the counting function N_bb(E) ~ E^\delta. For the stadium billiard we find agreement with the previous result \delta = 3/4. For the cosine billiard we derive \delta = 5/8, which is confirmed numerically and is well below the previously predicted upper bound \delta=9/10.
Keywords
Cite
@article{arxiv.1110.6307,
title = {Coupling of bouncing-ball modes to the chaotic sea and their counting function},
author = {Steffen Löck and Arnd Bäcker and Roland Ketzmerick},
journal= {arXiv preprint arXiv:1110.6307},
year = {2012}
}
Comments
10 pages, 6 figures