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December 2014 Systems of global surfaces of section for dynamically convex Reeb flows on the 3-sphere
Umberto L. Hryniewicz
J. Symplectic Geom. 12(4): 791-862 (December 2014).

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 three-dimensional energy levels.

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Umberto L. Hryniewicz. "Systems of global surfaces of section for dynamically convex Reeb flows on the 3-sphere." J. Symplectic Geom. 12 (4) 791 - 862, December 2014.

Information

Published: December 2014
First available in Project Euclid: 1 June 2015

zbMATH: 1334.53082
MathSciNet: MR3333029

Rights: Copyright © 2014 International Press of Boston

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Vol.12 • No. 4 • December 2014
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