Scarcity of Periodic Orbits in Outer Billiards

Research output: Contribution to journalArticlepeer-review


We give a simple proof of the result of Tumanov and Zharnitsky (Int Math Res Not, 2006) that the set of period 4 orbits in planar outer billiard with piecewise smooth convex boundary has empty interior, provided that no four corners of the boundary form a parallelogram. We also obtain results on period 5 and 6 orbits.

Original languageEnglish (US)
Pages (from-to)2479-2490
Number of pages12
JournalJournal of Geometric Analysis
Issue number3
StatePublished - Jul 1 2020


  • Exterior differential system
  • Outer billiard
  • Periodic orbit

ASJC Scopus subject areas

  • Geometry and Topology


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