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A lower bound for chaos on the elliptical stadium

✍ Scribed by Eduardo Canale; Roberto Markarian; Sylvie Oliffson Kamphorst; Sônia Pinto de Carvalho

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
620 KB
Volume
115
Category
Article
ISSN
0167-2789

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✦ Synopsis

The elliptical stadium is a plane region bounded by a curve constructed by joining two half-ellipses, with half axes a > 1 and b = 1, by two parallel segments of equal length 2h. proved that if I < a < ~ and ifh is large enough then the corresponding billiard map has non-vanishing Lyapunov exponents almost everywhere: moreover h -+ ~ as a -+ ~,/'2. In a previous paper [Markarian et al. Comm. Math. Phys. 174 (1996) 6,61-679[ we found a bound for h assuring the K-property for these billiards, for values of a very close to 1.

In this work we study the stability of a particular family of periodic orbits obtaining a new bound t~)r the chaotic zone for any value ofa < ~.

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