A Lower Bound for Chaos on the Elliptical Stadium

Details A Lower Bound for Chaos on the Elliptical Stadium A Lower Bound for Chaos on the Elliptical Stadium

1997-04-04

arxiv.org/abs/chao-dyn/9704006v1

Nonlinear Sciences

Chaotic Dynamics

13 pages, LaTeX. 7 postscript low resolution figures included. High resolution figures avaiable under request to syok@mat.ufmg

Scientific paper

10.1016/S0167-2789(97)00232-7

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.

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