English

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