Coadjoint orbits of area-preserving diffeomorphisms of non-orientable surfaces
Symplectic Geometry
2024-04-09 v2
Abstract
We give a classification of generic coadjoint orbits for the group of area-preserving diffeomorphisms of a closed non-orientable surface. This completes V. Arnold's program of studying invariants of incompressible fluids in 2D. As an auxiliary problem, we also classify simple Morse pseudo-functions on non-orientable surfaces up to area-preserving diffeomorphisms.
Keywords
Cite
@article{arxiv.2304.09354,
title = {Coadjoint orbits of area-preserving diffeomorphisms of non-orientable surfaces},
author = {Anton Izosimov and Boris Khesin and Ilia Kirillov},
journal= {arXiv preprint arXiv:2304.09354},
year = {2024}
}
Comments
27 pages, 3 figures; final version, to appear in Journal of Symplectic Geometry