In this work we address the question of proving the stability of elliptic 2-periodic orbits for strictly convex billiards. Even though it is part of a widely accepted belief that ellipticity implies stability, classical theorems show that the certainty of stability relies upon more precise conditions. We present a review of the main results and general theorems and describe the procedure to fulfill the supplementary conditions for strictly convex billiards.
@article{1128371755,
author = {Kamphorst, Sylvie Oliffson and Pinto-de-Carvalho, S\^onia},
title = {The first Birkhoff coefficient and the stability of 2-periodic orbits on billiards},
journal = {Experiment. Math.},
volume = {14},
number = {1},
year = {2005},
pages = { 299-306},
language = {en},
url = {http://dml.mathdoc.fr/item/1128371755}
}
Kamphorst, Sylvie Oliffson; Pinto-de-Carvalho, Sônia. The first Birkhoff coefficient and the stability of 2-periodic orbits on billiards. Experiment. Math., Tome 14 (2005) no. 1, pp. 299-306. http://gdmltest.u-ga.fr/item/1128371755/