Decorated Nonlinear Flags, Pointed Vortex Loops and the Dihedral Group

Ioana Ciuclea

doi:10.2478/awutm-2024-0004

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Decorated Nonlinear Flags, Pointed Vortex Loops and the Dihedral Group

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 60 (2024): Issue 1 (January 2024)

By: Ioana Ciuclea

Open Access

|Jun 2024

Abstract

We identify pointed vortex loops in the plane with low dimensional nonlinear flags decorated with volume forms. We show how submanifolds of such decorated nonlinear flags can be identified with coadjoint orbits of the area pre- serving diffeomorphism group and relate them to coadjoint orbits of pointed vortex loops. The subgroup of the dihedral group preserving the vorticity data plays a role in the description of these coadjoint orbits.

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