Journal of Symplectic Geometry

Volume 12 (2014)

Number 4

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

Pages: 791 – 862



Umberto L. Hryniewicz (Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal, Rio de Janeiro, Brazil)


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.

Published 27 March 2015