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

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

Daniel Genin, Serge Tabachnikov

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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.

Original language	English (US)
Pages (from-to)	155-173
Number of pages	19
Journal	Journal of Modern Dynamics
Volume	1
Issue number	2
DOIs	https://doi.org/10.3934/jmd.2007.1.155
State	Published - Apr 2007

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

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10.3934/jmd.2007.1.155

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

Abstract

All Science Journal Classification (ASJC) codes

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