New smooth counterexamples to the Hamiltonian Seifert conjecture

Details New smooth counterexamples to the Hamiltonian Seifert conjecture New smooth counterexamples to the Hamiltonian Seifert conjecture

2001-01-23

arxiv.org/abs/math/0101185v1

Mathematics

Differential Geometry

10 pages

Scientific paper

We construct a new aperiodic symplectic plug and hence new smooth counterexamples to the Hamiltonian Seifert conjecture in R^{2n} for n>2. In other words, we develop an alternative procedure, to those of V. L. Ginzburg and M. Herman, for constructing smooth Hamiltonian flows, on the standard symplectic R^{2n} for n>2, which have compact regular level sets that contain no periodic orbits. The plug described here is a modification of those built by Ginzburg. In particular, we utilize a different "trap" which makes the necessary embeddings of this plug much easier to construct.

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