Does a billiard orbit determine its (polygonal) table?

Volume 212 / 2011

Jozef Bobok, Serge Troubetzkoy Fundamenta Mathematicae 212 (2011), 129-144 MSC: Primary 37C15, 37E35. DOI: 10.4064/fm212-2-2

Abstract

We introduce a new equivalence relation on the set of all polygonal billiards. We say that two billiards (or polygons) are order equivalent if each of the billiards has an orbit whose footpoints are dense in the boundary and the two sequences of footpoints of these orbits have the same combinatorial order. We study this equivalence relation under additional regularity conditions on the orbit.

Authors

  • Jozef BobokKM FSv ČVUT
    Thákurova 7
    166 29 Praha 6, Czech Republic
    e-mail
  • Serge TroubetzkoyCentre de physique théorique
    Fédération de Recherches des Unités
    de Mathématique de Marseille
    Institut de mathématiques de Luminy
    and
    Université de la Méditerranée
    Luminy, Case 907
    F-13288 Marseille Cedex 9, France
    e-mail

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