Billiard Tables with rotational symmetry

Abstract: Consider the following simple geometric fact: the only centrally symmetric convex curve of constant width is a circle. The condition of having constant width is equivalent for the (Birkhoff) billiard map to have a 1-parameter family of two periodic orbits. We generalize this statement to curves that are invariant under a rotation by angle $\frac{2\pi}{k}$, for which the billiard map has a 1-parameter family of k-periodic orbits. We will also consider a similar setting for other billiard systems: outer billiards, symplectic billiards, and (a special case of) Minkowski billiards. Joint work with Misha Bialy.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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