16 research outputs found
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]
References
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