Spherical billiards with many 3periodic orbits
Spherical billiards with many 3periodic orbits

Yuliy Baryshnikov, Bell Laboratories
Fine Hall 401
It is known that the Lebesgue measure of 3periodic trajectories in a planar (Birkhoff) billiards is zero (and a wellknown conjecture states that the same is true for any period). On the sphere, however, it is easy to construct a billiard domain with 2dimensional family of 3periodic orbits (take the intersection of the sphere with the positive octant). In this talk I will explain why this is essentially the only possible construction.