2000/09/22 by Sylvie Oliffson Kamphorst, Kamphorst, Sylvie Oliffson, Sonia Pinto de Carvalho +2
Mathematics · Physics and Astronomy · #37C05 #37E40 #Algebraic and Geometric Analysis #Chaotic Dynamics (nlin.CD) #Differential Equations and Boundary Problems #Dynamical Systems (math.DS) #Electromagnetic Scattering and Analysis #FOS: Mathematics #FOS: Physical sciences #math.DS #msc:37C05 #msc:37E40 #nlin.CD
paper · pdf · doi:10.48550/arxiv.math/0009210
12 pages, 6 ps figures
arxiv created 2000/09/22 · openalex publication_date 2000/09/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the existence of elliptic islands for a special family of periodic orbits of a two-parameter family of maps corresponding to the billiard problem on the elliptical stadium. The hyperbolic or elliptical character of these orbits is also investigated. Depending on the parameters, we obtain upper bounds of ellipticity for this special family as a lower bound for chaos. On a different region of the parameter space, we can prove that there is no upper bound for the existence of elliptic islands. The main results we use are Birkhoff Normal Form and Moser's Twist Theorem.