New Smooth counterexamples to the Hamiltonian Seifert conjecture

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.