Angular Billiard and Algebraic Birkhoff conjecture
  In this paper we introduce a new dynamical system which we call Angular billiard. It acts on the exterior points of a convex curve in Euclidean plane. In a neighborhood of the boundary curve this system turns out to be dual to the Birkhoff billiard. Using this system we get new results on algebraic Birkhoff conjecture on integrable billiards. 
Michael Bialy and Andrey E. Mironov
math.DG math-ph math.MP nlin.SI