<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Decorated Nonlinear Flags, Pointed Vortex Loops and the Dihedral Group

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Decorated Nonlinear Flags, Pointed Vortex Loops and the Dihedral Group"}

We identify pointed vortex loops in the plane with low dimensional nonlinear flags decorated with volume forms. We show how submanifolds of such decorated...

Decorated Nonlinear Flags, Pointed Vortex Loops and the Dihedral Group

Published Online: Jun 07, 2024

Page range: 56 - 72

Received: May 17, 2024

Accepted: May 31, 2024

DOI: https://doi.org/10.2478/awutm-2024-0004

Keywords
nonlinear flags, coadjoint orbits, dihedral group, pointed vortex loops

© 2024 Ioana Ciuclea, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Decorated Nonlinear Flags, Pointed Vortex Loops and the Dihedral Group

Published Online: Jun 07, 2024

Page range: 56 - 72

Received: May 17, 2024

Accepted: May 31, 2024

DOI: https://doi.org/10.2478/awutm-2024-0004

Keywordsnonlinear flags, coadjoint orbits, dihedral group, pointed vortex loops

© 2024 Ioana Ciuclea, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
nonlinear flags, coadjoint orbits, dihedral group, pointed vortex loops