Spherical billiards with many 3-periodic orbits

Spherical billiards with many 3-periodic orbits

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Yuliy Baryshnikov, Bell Laboratories
Fine Hall 401

It is known that the Lebesgue measure of 3-periodic trajectories in a planar (Birkhoff) billiards is zero (and a well-known conjecture states that the same is true for any period). On the sphere, however, it is easy to construct a billiard domain with 2-dimensional family of 3-periodic 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.