Coadjoint orbits of area-preserving diffeomorphisms of non-orientable surfaces
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classification
math.SG
keywords
area-preservingdiffeomorphismsnon-orientablecoadjointorbitssurfacesarnoldauxiliary
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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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