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

Sylvie Oliffson Kamphorst·Sonia Pinto de Carvalho
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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.

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Sylvie Oliffson Kamphorst, Sonia Pinto de Carvalho. 2004-10-14. The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on Billiards. https://arxiv.org/abs/nlin/0410019

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