Hausdorff dimension of three-period orbits in Birkhoff billiards
Dynamical Systems
2015-06-03 v1 Chaotic Dynamics
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.
Keywords
Cite
@article{arxiv.1112.2745,
title = {Hausdorff dimension of three-period orbits in Birkhoff billiards},
author = {Sergei Merenkov and Vadim Zharnitsky},
journal= {arXiv preprint arXiv:1112.2745},
year = {2015}
}
Comments
10 pages, 1 figure