Coupling of bouncing-ball modes to the chaotic sea and their counting function

Details Coupling of bouncing-ball modes to the chaotic sea and their counting function Coupling of bouncing-ball modes to the chaotic sea and their counting function

2011-10-28

arxiv.org/abs/1110.6307v2

Phys. Rev. E 85, 016210 (2012)

Nonlinear Sciences

Chaotic Dynamics

10 pages, 6 figures

Scientific paper

10.1103/PhysRevE.85.016210

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.

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