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.


37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010)
37E99 Low-dimensional dynamical systems
70H05 Hamilton’s equations
Full Text: DOI arXiv Euclid EuDML Link