English

New smooth counterexamples to the Hamiltonian Seifert conjecture

Differential Geometry 2007-05-23 v1 Dynamical Systems Symplectic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.math/0101185,
  title  = {New smooth counterexamples to the Hamiltonian Seifert conjecture},
  author = {Ely Kerman},
  journal= {arXiv preprint arXiv:math/0101185},
  year   = {2007}
}

Comments

10 pages

R2 v1 2026-07-22T16:36:57.703Z