Stability and ergodicity of moon billiards.
We construct a two-parameter family of moon-shaped billiard tables with boundary made of two circular arcs. These tables fail the defocusing mechanism and other known mechanisms that guarantee ergodicity and hyperbolicity. We analytically study the stability of some periodic orbits and prove there is a class of billiards in this family with elliptic periodic orbits. These moon billiards can be viewed as generalization of annular billiards, which all have Kolmogorov-Arnold-Moser islands. However, the novelty of this paper is that by varying the parameters, we numerically observe a subclass of moon-shaped billiards with a single ergodic component.
CIMA-UE, Department of Mathematics, University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal.
Maria F
MF
Correia
Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts 01003-9305, USA.
Hong-Kun
HK
Zhang