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.
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