The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on Billiards
Chaotic Dynamics
2007-05-23 v1 Dynamical Systems
Abstract
In this work we address the question of proving the stability of elliptic 2-periodic orbits for strictly convex billiards. Eventhough it is part of a widely accepted belief that ellipticity implies stability, classical theorems show that the certainty of stability relies upon more fine conditions. We present a review of the main results and general theorems and describe the procedure to fullfill the supplementary conditions for strictly convex billiards.
Cite
@article{arxiv.nlin/0410019,
title = {The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on Billiards},
author = {Sylvie Oliffson Kamphorst and Sonia Pinto de Carvalho},
journal= {arXiv preprint arXiv:nlin/0410019},
year = {2007}
}
Comments
for programs see http://www.mat.ufmg.br/~syok/papers