Duality of caustics in Minkowski billiards

S. Artstein-Avidan, D. I. Florentin, Y. Ostrover, D. Rosen

Research output: Contribution to journalArticlepeer-review


In this paper we study convex caustics in Minkowski billiards. We show that for the Euclidean billiard dynamics in a planar smooth, centrally symmetric, strictly convex body K, for every convex caustic which K possesses, the 'dual' billiard dynamics in which the table is the Euclidean unit ball and the geometry that governs the motion is induced by the body K, possesses a dual convex caustic. Such a pair of caustics are dual in a strong sense, and in particular they have the same perimeter, Lazutkin parameter (both measured with respect to the corresponding geometries), and rotation number. We show moreover that for general Minkowski billiards this phenomenon fails, and one can construct a smooth caustic in a Minkowski billiard table which possesses no dual convex caustic.

Original languageEnglish
Pages (from-to)1197-1226
Number of pages30
Issue number4
StatePublished - 19 Feb 2018


  • Minkowski billiards
  • billiards
  • convex body, caustics


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