On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards

Details On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards

2006-04-18

arxiv.org/abs/math/0604388v1

Mathematics

Differential Geometry

Scientific paper

Following a recent paper by Baryshnikov and Zharnitskii, we consider outer
billiards in the plane possessing invariant curves consisting of periodic
orbits. We prove the existence and abundance of such tables using tools from
sub-Riemannian geometry. We also prove that the set of 3-periodic outer
billiard orbits has zero measure.

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