Does a billiard orbit determine its (polygonal) table?

• Autorzy: Jozef Bobok , Serge Troubetzkoy
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37E35: Flows on surfaces
• 37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 212
• Numer: 2
• Strony: 129-144

Daty

wydano

2011

Twórcy

autor

Jozef Bobok

• KM FSv ČVUT, Thákurova 7, 166 29 Praha 6, Czech Republic

autor

Serge Troubetzkoy

• Centre de physique théorique, Fédération de Recherches des Unités de Mathématique de Marseille, Institut de mathématiques de Luminy, Université de la Méditerranée, Luminy, Case 907, F-13288 Marseille Cedex 9, France

Identyfikatory

DOI

10.4064/fm212-2-2