Symmetric periodic orbits in symmetric billiards

In this text we study billiards on symmetric ovals and investigate some consequences of the symmetry of the boundary on the dynamics. As it simplifies some calculations, the symmetry helps to obtain the results. We focus on periodic orbits with the same symmetry of the boundary which always exist an...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinearity 2024-12, Vol.37 (1), p.15005
Main Authors: Ferreira, Geraldo César Gonçalves, Oliffson Kamphorst, Sylvie, Pinto-de-Carvalho, Sônia
Format: Article
Language:English
Subjects:
37C20
37C79
37C83
billiards
elliptic islands
non integrability
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this text we study billiards on symmetric ovals and investigate some consequences of the symmetry of the boundary on the dynamics. As it simplifies some calculations, the symmetry helps to obtain the results. We focus on periodic orbits with the same symmetry of the boundary which always exist and prove that typically half of them are elliptic and Moser stable and the other half are hyperbolic with homo(hetero)clinic intersections.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/ad0c94