2002/01/11 by Mário Carneiro, Mario Jorge Dias Carneiro, Carneiro, Mario Jorge Dias +5 · 1 citation
Mathematics · Physics and Astronomy · #37C05 #37E40 #70K42 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #math.DS #msc:37C05 #msc:37E40 #msc:70K42
paper · pdf · doi:10.48550/arxiv.math/0201096
12 pages, 6 figures
arxiv created 2002/01/11 · openalex publication_date 2002/01/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper addresses the question of genericity of existence of elliptic islands for the billiard map associated to strictly convex closed curves. More precisely, we study 2-periodic orbits of billiards associated to C5 closed and strictly convex curves and show that the existence of elliptic islands is a dense property on the subset of those billiards having an elliptic 2-periodic point. Our main tools are normal perturbations, the Birkhoff Normal Form for elliptic fixed points and Moser's Twist Theorem.