New publication on periodic orbits in billiards

The journal Annales Henri Poincaré recently published a new paper on mathematical billiards by former VU students Casper Oelen (now at Heriot-Watt), Mattia Sensi (now at the University of Trento), and Bob Rink (ACDC).  

A classical theorem by Poincaré and Birkhoff from the 1920s guarantees that every convex billiard admits two periodic orbits with the shape of any imaginable polygon or star-polygon (e.g., triangle, square, pentagon, pentagram, etc.) The paper finds conditions under which a convex symmetric billiard admits more complicated periodic orbits such as the ones in the figures above. This result may help towards solving the famous Birkhoff conjecture, which states that any convex billiard that does not have the shape of an ellipse must be non-integrable or even chaotic.