Code & order in polygonal billiards
  Two polygons $P,Q$ are code equivalent if there are billiard orbits $u,v$ which hit the same sequence of sides and such that the projections of the orbits are dense in the boundaries $\partial P, \partial Q$. Our main results show when code equivalent polygons have the same angles, resp. are similar, resp. affinely similar. 
Jozef Bobok, Serge Troubetzkoy (FRUMAM, CPT, IML)
math.DS