Pseudorotations of the 2-disc and Reeb flows on the 3-sphere - Albers, Peter; Geiges, Hansjörg; Zehmisch, Kai (Arxiv, 2018)
We use Lerman's contact cut construction to find a sufficient condition for Hamiltonian diffeomorphisms of compact surfaces to embed into a closed 3-manifold as Poincaré return maps on a global surface of section for a Reeb flow. In particular, we show that the irrational pseudorotations of the 2-disc constructed by Fayad-Katok embed into the Reeb flow of a dynamically convex contact form on the 3-sphere.