1 results
Pseudorotations of the
$2$
-disc and Reeb flows on the 
$3$
-sphere
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 42 / Issue 2 / February 2022
- Published online by Cambridge University Press:
- 18 March 2021, pp. 402-436
- Print publication:
- February 2022
-
- Article
- Export citation
-
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 and Katok embed into the Reeb flow of a dynamically convex contact form on the
$3$
-sphere.
