A smooth counterexample to the Hamiltonian Seifert conjecture in R^6
Abstract
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.
- Publication:
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eprint arXiv:dg-ga/9703006
- Pub Date:
- March 1997
- DOI:
- 10.48550/arXiv.dg-ga/9703006
- arXiv:
- arXiv:dg-ga/9703006
- Bibcode:
- 1997dg.ga.....3006G
- Keywords:
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- Mathematics - Differential Geometry;
- 58Exx
- E-Print:
- AMS-LaTeX, 11 pages, substantially revised, to appear in IMRN