Commuting dual billiard maps

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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

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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