Pseudorotations of the 2-disc and Reeb flows on the 3-sphere
Dynamical Systems
2023-02-07 v3 Symplectic Geometry
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 Poincar\'e 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.
Keywords
Cite
@article{arxiv.1804.07129,
title = {Pseudorotations of the 2-disc and Reeb flows on the 3-sphere},
author = {Peter Albers and Hansjörg Geiges and Kai Zehmisch},
journal= {arXiv preprint arXiv:1804.07129},
year = {2023}
}
Comments
30 pages; v2: Section 2 rewritten; v3: small changes to the exposition, some references added