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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1947-1954 |
| Number of pages | 8 |
| Journal | Nonlinearity |
| Volume | 25 |
| Issue number | 7 |
| DOIs | |
| State | Published - Jul 2012 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics