The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on Billiards

Details The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on Billiards The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on Billiards

2004-10-14

arxiv.org/abs/nlin/0410019v1

Nonlinear Sciences

Chaotic Dynamics

for programs see http://www.mat.ufmg.br/~syok/papers

Scientific paper

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.

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