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

Daniel Genin; Serge Tabachnikov

doi:10.3934/jmd.2007.1.155

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2007, Volume 1, Issue 2: 155-173. Doi: 10.3934/jmd.2007.1.155

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

Daniel Genin^1, and
Serge Tabachnikov^1,

1.
Department of Mathematics, Penn State University, University Park, PA 16802

Received: March 31, 2006

Published: December 2006

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Abstract

Following a recent paper by Baryshnikov and Zharnitsky, 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 empty interior.

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Mathematics Subject Classification: Primary 53C17, 37J45.

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