Scarcity of Periodic Orbits in Outer Billiards

Alexander Tumanov

doi:10.1007/s12220-017-9927-8

Scarcity of Periodic Orbits in Outer Billiards

Alexander Tumanov

Mathematics

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

Abstract

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 language	English (US)
Pages (from-to)	2479-2490
Number of pages	12
Journal	Journal of Geometric Analysis
Volume	30
Issue number	3
DOIs	https://doi.org/10.1007/s12220-017-9927-8
State	Published - Jul 1 2020

Keywords

Exterior differential system
Outer billiard
Periodic orbit

ASJC Scopus subject areas

Geometry and Topology

Online availability

10.1007/s12220-017-9927-8

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abstract = "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.",

keywords = "Exterior differential system, Outer billiard, Periodic orbit",

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AB - 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.

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KW - Periodic orbit

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Scarcity of Periodic Orbits in Outer Billiards

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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