A smooth counterexample to the Hamiltonian Seifert conjecture in R^6
| dc.creator | Ginzburg, Viktor L. | |
| dc.date | 1997-03-09 | |
| dc.date | 1997-06-21 | |
| dc.date.accessioned | 2026-07-07T08:59:13Z | |
| dc.date.available | 2026-07-07T08:59:13Z | |
| dc.description | A smooth counterexample to the Hamiltonian Seifert conjecture for six-dimensional symplectic manifolds is found. In particular, we construct a smooth proper function on the symplectic 2n-dimensional vector space, 2n > 4, such that one of its non-singular level sets carries no periodic orbits of the Hamiltonian flow. The function can be taken to be C^0-close and isotopic to a positive-definite quadratic form so that the level set in question is isotopic to an ellipsoid. This is a refinement of previously known constructions giving such functions for 2n > 6. The proof is based on a new version of a symplectic embedding theorem applied to the horocycle flow. | |
| dc.description | AMS-LaTeX, 11 pages, substantially revised, to appear in IMRN | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9703006 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9703006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147627 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58Exx | |
| dc.title | A smooth counterexample to the Hamiltonian Seifert conjecture in R^6 | |
| dc.type | text |