Systems of global surfaces of section for dynamically convex Reeb flows   on the 3-sphere
  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. 
Umberto Hryniewicz
math.SG math.DS