Commuting dual billiard maps

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

To a closed convex smooth curve in the plane the dual billiard transformation of its exterior corresponds: given a point outside of the curve, draw a tangent line to it through the point, and reflect the point in the point of tangency. We prove that if two curves are given, such that the corresponding dual billiard transformations commute, then the curves are concentric homothetic ellipses.

Original languageEnglish (US)
Pages (from-to)57-68
Number of pages12
JournalGeometriae Dedicata
Volume53
Issue number1
DOIs
StatePublished - Nov 1 1994

Fingerprint

Billiards
Curve
Concentric
Commute
Tangent line
Closed

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Tabachnikov, Sergei. / Commuting dual billiard maps. In: Geometriae Dedicata. 1994 ; Vol. 53, No. 1. pp. 57-68.
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Commuting dual billiard maps. / Tabachnikov, Sergei.

In: Geometriae Dedicata, Vol. 53, No. 1, 01.11.1994, p. 57-68.

Research output: Contribution to journalArticle

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