Differentiable rigidity and smooth conjugacy.
Diophantine classes, dimension and Denjoy maps
Does a billiard orbit determine its (polygonal) table?
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.