Geodesic
Does a billiard orbit determine its (polygonal) table?
Jozef Bobok 1   ; Serge Troubetzkoy 2
1 KM FSv ČVUT Thákurova 7 166 29 Praha 6, Czech Republic
2 Centre 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
Fundamenta Mathematicae, Tome 212 (2011) no. 2, pp. 129-144 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm212-2-2
Keywords: introduce equivalence relation set polygonal billiards say billiards polygons order equivalent each billiards has orbit whose footpoints dense boundary sequences footpoints these orbits have combinatorial order study equivalence relation under additional regularity conditions orbit

Jozef Bobok  1   ; Serge Troubetzkoy  2

1 KM FSv ČVUT Thákurova 7 166 29 Praha 6, Czech Republic
2 Centre 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 
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Jozef Bobok; Serge Troubetzkoy. Does a billiard orbit determine its (polygonal) table?. Fundamenta Mathematicae, Tome 212 (2011) no. 2, pp. 129-144. doi: 10.4064/fm212-2-2

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