Does a billiard orbit determine its (polygonal) table?
Volume 212 / 2011
Fundamenta Mathematicae 212 (2011), 129-144 MSC: Primary 37C15, 37E35. DOI: 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 under additional regularity conditions on the orbit.