Systems of global surfaces of section for dynamically convex Reeb flows on the 3-sphere
Symplectic Geometry
2015-02-09 v5 Dynamical Systems
Abstract
We characterize which closed Reeb orbits of a dynamically convex contact form on the 3-sphere bound disk-like global surfaces of section for the Reeb flow, without any genericity assumptions. We show that these global surfaces of section come in families, organized as open book decompositions. As an application we obtain new global surfaces of section for the Hamiltonian dynamics on strictly convex 3-dimensional energy levels.
Keywords
Cite
@article{arxiv.1105.2077,
title = {Systems of global surfaces of section for dynamically convex Reeb flows on the 3-sphere},
author = {Umberto Hryniewicz},
journal= {arXiv preprint arXiv:1105.2077},
year = {2015}
}
Comments
Statement of Lemma 3.16 is corrected, as well as the discussion following it. To appear in the Journal of Symplectic Geometry