Hyperbolicity of asymmetric lemon billiards

Asymmetric lemon billiards was introduced in Chen et al (2013 Chaos 23 043137), where the billiard table Q(r, b, R) is the intersection of two round disks with radii r ⩽ R, respectively, and b measures the distance between the two centres. It is conjectured Bunimovich et al (2016 Commun. Math. Phys. 341 781–803) that the asymmetric lemon billiards is hyperbolic when the arc Γ_r is a major arc and R is large. In this paper we prove this conjecture for sufficiently large R. (paper)