Hausdorff dimension of three-period orbits in Birkhoff billiards
  We prove that the Hausdorff dimension of the set of three-period orbits in classical billiards is at most one. Moreover, if the set of three-period orbits has Hausdorff dimension one, then it has a tangent line at almost every point. 
Sergei Merenkov, Vadim Zharnitsky
math.DS nlin.CD