Coadjoint orbits of symplectic diffeomorphisms of surfaces and ideal hydrodynamics

Anton Izosimov, Boris Khesin, Mehdi Mousavi

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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

Original languageEnglish (US)
Pages (from-to)2385-2433
Number of pages49
JournalAnnales de l'Institut Fourier
Issue number6
StatePublished - 2016


  • Casimirs
  • Circulations
  • Coadjoint orbits
  • Hamiltonian diffeomorphisms
  • Isovorticed fields
  • Measured Reeb graphs
  • Pants decomposition
  • Simple Morse functions
  • Symplectic diffeomorphisms
  • Vorticity function

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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