@article{4b876e8e1af64ea7b3d0908ac2ccbc08,
title = "On configuration spaces of plane polygons, sub-riemannian geometry and periodic orbits of outer billiards",
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.",
author = "Daniel Genin and Serge Tabachnikov",
note = "Funding Information: We are grateful to Yu. Baryshnikov, S. Lvovski, R. Montgomery, K. F. Siburg, V. Zharnitsky for stimulating discussions and to the referees for their numerous suggestions that improved the exposition. The second author is indebted to Max-Planck-Institut in Bonn for its invariable hospitality. Partially supported by NSF grant DMS-0555803. Publisher Copyright: {\textcopyright} 2007 AIMSCIENCES.",
year = "2007",
month = apr,
doi = "10.3934/jmd.2007.1.155",
language = "English (US)",
volume = "1",
pages = "155--173",
journal = "Journal of Modern Dynamics",
issn = "1930-5311",
publisher = "American Institute of Mathematical Sciences",
number = "2",
}