A smooth counterexample to the Hamiltonian Seifert conjecture in R^6

Details A smooth counterexample to the Hamiltonian Seifert conjecture in R^6 A smooth counterexample to the Hamiltonian Seifert conjecture in R^6

1997-03-09

arxiv.org/abs/dg-ga/9703006v3

Mathematics

Differential Geometry

AMS-LaTeX, 11 pages, substantially revised, to appear in IMRN

Scientific paper

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.

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