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The first Birkhoff coefficient and the stability of 2-periodic orbits on billiards. (English) Zbl 1159.37423

Summary: 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.

MSC:

37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010)
37E99 Low-dimensional dynamical systems
70H05 Hamilton’s equations
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