A Lower Bound for Chaos on the Elliptical Stadium

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.Comment: 13 pages, LaTeX. 7 postscript low resolution figures included. High resolution figures avaiable under request to [email protected]

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The elliptical stadium is a plane region bounded by a curve \Gamma, constructed by joining two half-ellipses, with major axes a? 1 and minor axes b = 1, by two straight segments of equal length 2h. The billiard on the elliptical stadium consists in the study of the free motion of a point particle inside the stadium, being reflected elastically at the impacts with \Gamma