Coadjoint orbits of symplectic diffeomorphisms of surfaces and ideal\n hydrodynamics

2015/04/21 by Anton Izosimov, Izosimov, Anton, Boris Khesin +3
Earth and Planetary Sciences · Mathematics · #Computer science #Discrete mathematics #FOS: Mathematics #Geology and Paleoclimatology Research #Geometry and complex manifolds #Graph #Hamiltonian (control theory) #Hamiltonian system #Ideal (ethics) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematical optimization #Mathematics #Moment map #Morse code #Pure mathematics #Simple (philosophy) #Symplectic Geometry (math.SG) #Symplectic geometry #Symplectic matrix #Symplectic representation #Symplectomorphism #math.SG

paper · pdf · doi:10.48550/arxiv.1504.05629

38 pages, 11 figures; to appear in Annales de l'Institut Fourier

openalex publication_date 2015/04/21 · arxiv created 2016/03/28 · arxiv updated 2016/03/30 · openalex created_date 2022/10/02 · openalex updated_date 2026/08/05

Abstract

We give a classification of generic coadjoint orbits for the groups of\nsymplectomorphisms and Hamiltonian diffeomorphisms of a closed symplectic\nsurface. We also classify simple Morse functions on symplectic surfaces with\nrespect to actions of those groups. This gives an answer to V.Arnold's problem\non describing all invariants of generic isovorticed fields for the 2D ideal\nfluids. For this we introduce a notion of anti-derivatives on a measured Reeb\ngraph and describe their properties.\n

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