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Journal of Modern Dynamics (JMD)
 

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

Pages: 155 - 173, Issue 2, April 2007      doi:10.3934/jmd.2007.1.155

 
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Daniel Genin - Department of Mathematics, Penn State University, University Park, PA 16802, United States (email)
Serge Tabachnikov - Department of Mathematics, Penn State University, University Park, PA 16802, United States (email)

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.

Keywords:  outer billiards, invariant curves, sub-Riemannian geometry
Mathematics Subject Classification:  Primary 53C17, 37J45.

Received: April 2006;      Available Online: January 2007.