Hyperbolicity of asymmetric lemon billiards

Abstract

Asymmetric lemon billiards was introduced in [CMZZ], where the billiard table $Q(r,b,R)$ is the intersection of two round disks with radii $r\le R$, respectively, and $b$ measures the distance between the two centers. It is conjectured [BZZ] that the asymmetric lemon billiards is hyperbolic when the arc ${\Gamma }_r$ is a major arc and $R$ is large. In this paper we prove this conjecture for sufficiently large $R$.

Cited by in corpus (2)

• Homoclinic and heteroclinic intersections for lemon billiards
• Chaotic properties for billiards in circular polygons