Chaotic dynamics of the elliptical stadium billiard in the full parameter space
arXiv:nlin/0507014 · doi:10.1016/j.physd.2006.03.014
Abstract
Dynamical properties of the elliptical stadium billiard, which is a generalization of the stadium billiard and a special case of the recently introduced mushroom billiards, are investigated analytically and numerically. In dependence on two shape parameters delta and gamma, this system reveals a rich interplay of integrable, mixed and fully chaotic behavior. Poincare sections, the box counting method and the stability analysis determine the structure of the parameter space and the borders between regions with different behavior. Results confirm the existence of a large fully chaotic region surrounding the straight line delta=1-gamma corresponding to the Bunimovich circular stadium billiard. Bifurcations due to the hour-glass and multidiamond orbits are described. For the quantal elliptical stadium billiard, statistical properties of the level spacing fluctuations are examined and compared with classical results.
REVTEX4: 19 pages; JPG: 18 figures
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- Dynamical properties of a particle in a wave packet: scaling invariance and boundary crisis
- Numerical exploration of a hexagonal string billiard
- Chaotic properties of the truncated elliptical billiard
- Classical and Quantum Elliptical Billiards: Mixed Phase Space and Short Correlations in Singlets and Doublets