Hausdorff dimension of three-period orbits in Birkhoff billiards
arXiv:1112.2745 · doi:10.1088/0951-7715/25/7/1947
Abstract
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.
10 pages, 1 figure