A Lower Bound for Chaos on the Elliptical Stadium
arXiv:chao-dyn/9704006 · doi:10.1016/S0167-2789(97)00232-7
Abstract
The elliptical stadium is a plane region bounded by a curve constructed by joining two half-ellipses by two parallel segments of equal length. The billiard inside it, as a map, generates a two parameters family of dynamical systems. It is known that the system is ergodic for a certain region of the parameter space. In this work we study the stability of a particular family of periodic orbits obtaining good bounds for the chaotic zone.
arXiv comment13 pages, LaTeX. 7 postscript low resolution figures included. High resolution figures avaiable under request to [email protected]
References in corpus (1)
Cited by in corpus (6)
- The Fermi-Ulam Accelerator Model Under Scaling Analysis
- Chaotic dynamics of the elliptical stadium billiard in the full parameter space
- Chaos and stability in a two-parameter family of convex billiard tables
- Chaotic properties of the truncated elliptical billiard
- Classical and Quantum Elliptical Billiards: Mixed Phase Space and Short Correlations in Singlets and Doublets
- Hyperbolicity and Abundance of Elliptical Islands in Annular Billiards