Does a billiard orbit determine its (polygonal) table?

Jozef Bobok (1, 2, 3) , Serge Troubetzkoy (1, 4, 5, 3)

1 CPT - Centre de Physique Théorique - UMR 6207
2 KM FSv CVUT
3 CPT - Centre de Physique Théorique - UMR 7332
4 IML - Institut de mathématiques de Luminy
5 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille

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 with additional regularity conditions on the orbit.

Domaines: Systèmes dynamiques [math.DS]

Jozef Bobok, Serge Troubetzkoy. Does a billiard orbit determine its (polygonal) table?. Fund. Math., 2011, 212, pp.129-144. ⟨10.4064/fm212-2-2⟩. ⟨hal-00337472v2⟩