A smooth counterexample to the Hamiltonian Seifert conjecture in R^6
Abstract
A smooth counterexample to the Hamiltonian Seifert conjecture for sixdimensional symplectic manifolds is found. In particular, we construct a smooth proper function on the symplectic 2ndimensional vector space, 2n > 4, such that one of its nonsingular level sets carries no periodic orbits of the Hamiltonian flow. The function can be taken to be C^0close and isotopic to a positivedefinite 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:

eprint arXiv:dgga/9703006
 Pub Date:
 March 1997
 DOI:
 10.48550/arXiv.dgga/9703006
 arXiv:
 arXiv:dgga/9703006
 Bibcode:
 1997dg.ga.....3006G
 Keywords:

 Mathematics  Differential Geometry;
 58Exx
 EPrint:
 AMSLaTeX, 11 pages, substantially revised, to appear in IMRN