Elliptic Islands on Strictly Convex Billiards

Details Elliptic Islands on Strictly Convex Billiards Elliptic Islands on Strictly Convex Billiards

2002-01-11

arxiv.org/abs/math/0201096v1

Mathematics

Dynamical Systems

12 pages, 6 figures

Scientific paper

This paper addresses the question of genericity of existence of elliptic islands for the billiard map associated to strictly convex closed curves. More precisely, we study 2-periodic orbits of billiards associated to C5 closed and strictly convex curves and show that the existence of elliptic islands is a dense property on the subset of those billiards having an elliptic 2-periodic point. Our main tools are normal perturbations, the Birkhoff Normal Form for elliptic fixed points and Moser's Twist Theorem.

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