Elliptic Islands on Strictly Convex Billiards
Dynamical Systems
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0201096,
title = {Elliptic Islands on Strictly Convex Billiards},
author = {Mario Jorge Dias Carneiro and Sylvie Oliffson Kamphorst and Sonia Pinto De Carvalho},
journal= {arXiv preprint arXiv:math/0201096},
year = {2007}
}
Comments
12 pages, 6 figures