Chaotic Properties of the Elliptical Stadium Roberto Markarian

@inproceedings{Kamphorst1995ChaoticPO,
  title={Chaotic Properties of the Elliptical Stadium Roberto Markarian},
  author={Sylvie Oliffson Kamphorst},
  year={1995}
}
The elliptical stadium is a curve constructed by joining two half-ellipses, with half axes a > 1 and b = 1, by two straight segments of equal length 2h. Donnay [6] has shown that if 1 < a < √ 2 and if h is big enough, then the corresponding billiard map has a positive Lyapunov exponent almost everywhere; moreover, h → ∞ as a → √ 2. In this work we prove that if 1 < a < √ 4 − 2 √ 2, then h > 2a √ a − 1 assures the positiveness of a Lyapunov exponent. And we conclude that, for these values of a… CONTINUE READING