Journal of Symplectic Geometry

Volume 1 (2001)

Number 2

New Smooth counterexamples to the Hamiltonian Seifert conjecture

Pages: 253 – 268

DOI: http://dx.doi.org/10.4310/JSG.2001.v1.n2.a3

Author

Ely Kerman

Abstract

We construct a new aperiodic symplectic plug and hence new smooth counterexamples to the Hamiltonian Seifert conjecture in ℝ2n for n ≥ 3. In other words, we describe an alternative procedure, to those of V.L. Ginzburg [Gi1, Gi2] and M. Herman [Her], for producing smooth Hamiltonian flows, on symplectic manifolds of dimension at least six, 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 use a different "trap" which makes the necessary embeddings of this plug much easier to construct.

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