Article contents
Pseudorotations of the
$2$-disc and Reeb flows on the
$3$-sphere
Published online by Cambridge University Press: 18 March 2021
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 and Katok embed into the Reeb flow of a dynamically convex contact form on the
$3$
-sphere.
Keywords
MSC classification
- Type
- Original Article
- Information
- Ergodic Theory and Dynamical Systems , Volume 42 , Issue 2: Anatole Katok Memorial Issue Part 1: Special Issue of Ergodic Theory and Dynamical Systems , February 2022 , pp. 402 - 436
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
Footnotes
To the memory of Anatole Katok
References
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