On conformal points of area preserving maps and related topics

• Verfasst von: Albers, Peter [VerfasserIn]
• Verfasst von: Tabachnikov, Serge [VerfasserIn]
• Titel: On conformal points of area preserving maps and related topics
• Verf.angabe: Peter Albers, Serge Tabachnikov
• E-Jahr: 2022
• Jahr: 8 August 2022
• Umfang: 11 S.
• Fussnoten: Online veröffentlicht am 8 August 2022, Artikelversion 17 August 2022 ; Gesehen am 09.12.2022
• Titel Quelle: Enthalten in: Journal of geometry and physics
• Ort Quelle: Amsterdam [u.a.] : North-Holland, 1984
• Jahr Quelle: 2022
• Band/Heft Quelle: 180(2022), Artikel-ID 104644, Seite 1-11
• DOI: doi:10.1016/j.geomphys.2022.104644
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Area preserving maps
• Sach-SW: Carathéodory conjecture
• Sach-SW: Conformal points
• Sach-SW: Loewner conjecture
• K10plus-PPN: 1826705333

Abstract

In this article we consider area preserving diffeomorphisms of planar domains, and we are interested in their conformal points, i.e., points at which the derivative is a similarity. We present some conditions that guarantee existence of conformal points for the infinitesimal problem of Hamiltonian vector fields as well as for what we call moderate symplectomorphisms of simply connected domains. We also link this problem to the Carathéodory and Loewner conjectures.