Generic Oval Billiards

Details Generic Oval Billiards Generic Oval Billiards

2007-05-07

arxiv.org/abs/0705.0948v1

Mathematics

Dynamical Systems

14 pages with 1 figure

Scientific paper

In this paper we show that, under certain generic conditions, billiards on ovals have only a finite number of periodic orbits, for each period, all non-degenerate and at least one of them is hyperbolic. Moreover, the invariant curves of two hyperbolic points are transversal. We explore these properties to give some dynamical consequences specially about the dynamics in the instability regions.

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