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

Daniel Genin, Serge Tabachnikov

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)155-173
Number of pages19
JournalJournal of Modern Dynamics
Volume1
Issue number2
DOIs
StatePublished - Apr 2007

Fingerprint

Sub-Riemannian Geometry
Billiards
Configuration Space
Periodic Orbits
Polygon
Orbits
Invariant Curves
Geometry
Plane Curve
Tables
Interior
Orbit

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

Cite this

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On configuration spaces of plane polygons, sub-riemannian geometry and periodic orbits of outer billiards. / Genin, Daniel; Tabachnikov, Serge.

In: Journal of Modern Dynamics, Vol. 1, No. 2, 04.2007, p. 155-173.

Research output: Contribution to journalArticle

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