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

• Verfasst von: Albers, Peter [VerfasserIn]
• Verfasst von: Geiges, Hansjörg [VerfasserIn]
• Verfasst von: Zehmisch, Kai [VerfasserIn]
• Titel: Pseudorotations of the 2-disc and Reeb flows on the 3-sphere
• Verf.angabe: Peter Albers, Hansjörg Geiges, and Kai Zehmisch
• Jahr: 2022
• Umfang: 35 S.
• Fussnoten: Published online by Cambridge University Press: 18 March 2021 ; Gesehen am 12.07.2022
• Titel Quelle: Enthalten in: Ergodic theory and dynamical systems
• Ort Quelle: Cambridge, Mass. : Cambridge Univ. Press, 1981
• Jahr Quelle: 2022
• Band/Heft Quelle: 42(2022), 2, Seite 402-436
• ISSN Quelle: 1469-4417
• DOI: doi:10.1017/etds.2021.15
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 37J05
• Sach-SW: 37J55
• Sach-SW: 53D35
• Sach-SW: area-preserving diffeomorphisms of the disc
• Sach-SW: contact cut
• Sach-SW: global surface of section
• Sach-SW: open book decomposition
• Sach-SW: pseudorotation
• K10plus-PPN: 1809933099

Abstract

We use Lerman’s contact cut construction to find a sufficient condition for Hamiltonian diffeomorphisms of compact surfaces to embed into a closed -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 - -disc constructed by Fayad and Katok embed into the Reeb flow of a dynamically convex contact form on the - -sphere.