Pseudorotations of the 2-disc and Reeb flows on the 3-sphere

Abstract

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.

30 pages; v2: Section 2 rewritten; v3: small changes to the exposition, some references added

References in corpus (3)

• Sharp systolic inequalities for Reeb flows on the three-sphere
• On the contact mapping class group of Legendrian circle bundles
• The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closed

Cited by in corpus (3)

• Contact three-manifolds with exactly two simple Reeb orbits
• What does a vector field know about volume?
• Invariant Sets and Hyperbolic Closed Reeb Orbits