Systems of global surfaces of section for dynamically convex Reeb flows on the 3-sphere

2011/05/11 by Umberto Hryniewicz, Hryniewicz, Umberto · 1 citation
Mathematics · #37J99 #53D35 #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DS #math.SG #msc:37J99 #msc:53D35

paper · pdf · doi:10.48550/arxiv.1105.2077

Statement of Lemma 3.16 is corrected, as well as the discussion following it. To appear in the Journal of Symplectic Geometry

arxiv created 2015/02/06 · arxiv updated 2015/02/09

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.

Cited by

• On the knot types of periodic Reeb orbits of dynamically convex contact forms

Related

• Global surfaces of section with positive genus for dynamically convex Reeb flows
• A Reeb flow on the three-sphere without a disk-like global surface of\n section
• Global surfaces of section for Reeb flows in dimension three and beyond
• Global surfaces of section for dynamically convex Reeb flows on lens\n spaces
• Symmetric periodic orbits and invariant disk-like global surfaces of section on the three-sphere