Closed Reeb orbits on the sphere and symplectically degenerate maxima
Symplectic Geometry
2012-10-19 v1 Dynamical Systems
Abstract
We show that the existence of one simple closed Reeb orbit of a particular type (a symplectically degenerate maximum) forces the Reeb flow to have infinitely many periodic orbits. We use this result to give a different proof of a recent theorem of Cristofaro-Gardiner and Hutchings asserting that every Reeb flow on the standard contact three-sphere has at least two periodic orbits. Our methods are based on adapting the machinery originally developed for proving the Hamiltonian Conley conjecture to the contact setting.
Keywords
Cite
@article{arxiv.1210.5037,
title = {Closed Reeb orbits on the sphere and symplectically degenerate maxima},
author = {Viktor L. Ginzburg and Doris Hein and Umberto L. Hryniewicz and Leonardo Macarini},
journal= {arXiv preprint arXiv:1210.5037},
year = {2012}
}