Coadjoint orbits of area-preserving diffeomorphisms of non-orientable surfaces

2023/04/19 by Anton Izosimov, Izosimov, Anton, Boris Khesin +3
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2304.09354

openalex publication_date 2023/04/19 · openalex created_date 2023/04/22 · openalex updated_date 2026/07/28

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.

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