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

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April 2007, 1(2): 155-173. doi: 10.3934/jmd.2007.1.155

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, United States, United States

Received April 2006 Published January 2007

Abstract
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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.

Keywords: outer billiards, sub-Riemannian geometry, invariant curves.

Mathematics Subject Classification: Primary 53C17, 37J4.

Citation: Daniel Genin, Serge Tabachnikov. On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards. Journal of Modern Dynamics, 2007, 1 (2) : 155-173. doi: 10.3934/jmd.2007.1.155

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