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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.
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- 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
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