Does a billiard orbit determine its (polygonal) table?

Details Does a billiard orbit determine its (polygonal) table? Does a billiard orbit determine its (polygonal) table?

2008-11-07

arxiv.org/abs/0811.1094v2

Fund. Math. 212 (2011) 129-144

Mathematics

Dynamical Systems

Scientific paper

10.4064/fm212-2-2

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.

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