Symmetric periodic orbits in symmetric billiards

Abstract

In this text we study billiards on ovals and investigate some consequences of a rotational 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 in general half of them are elliptic and Moser stable and the other half are hyperbolic with homo(hetero)clinic intersections.

References in corpus (6)

• Capillary floating and the billiard ball problem
• On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces
• Chaotic Properties of the Elliptical Stadium
• Homoclinic points for convex billiards
• Elliptic Flowers: simply connected billiard tables with chaotic or non-chaotic flows moving around chaotic or non-chaotic cores
• Birkhoff Normal Form and Twist Coefficients of Periodic Orbits of Billiards

Cited by in corpus (1)

• Non-Birkhoff periodic orbits in symmetric billiards