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.
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| Veröffentlicht in: | Nonlinearity 2012-07, Vol.25 (7), p.1947-1954 |
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| container_end_page | 1954 |
|---|---|
| container_issue | 7 |
| container_start_page | 1947 |
| container_title | Nonlinearity |
| container_volume | 25 |
| creator | MERENKOV, Sergei ZHARNITSKY, Vadim |
| description | 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. |
| doi_str_mv | 10.1088/0951-7715/25/7/1947 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 0951-7715 |
| ispartof | Nonlinearity, 2012-07, Vol.25 (7), p.1947-1954 |
| issn | 0951-7715 1361-6544 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1730078810 |
| source | Institute of Physics Journals |
| subjects | Exact sciences and technology Global analysis, analysis on manifolds Mathematical methods in physics Mathematics Nonlinearity Orbits Other topics in mathematical methods in physics Physics Sciences and techniques of general use Tangents Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Hausdorff dimension of three-period orbits in Birkhoff billiards |
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