12 citations · 48 across the 26 of their papers we have counts for
6 papers · 1 filter
Coadjoint orbits of area-preserving diffeomorphisms of non-orientable surfaces
Anton Izosimov, Boris Khesin, Ilia Kirillov
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 stud…
Smooth invariants of focus-focus singularities and obstructions to product decomposition
Alexey Bolsinov, Anton Izosimov
We study focus-focus singularities (also known as nodal singularities, or pinched tori) of Lagrangian fibrations on symplectic -manifolds. We show that, in contrast to elliptic…
Vortex sheets and diffeomorphism groupoids
Anton Izosimov, Boris Khesin
In 1966 V.Arnold suggested a group-theoretic approach to ideal hydrodynamics in which the motion of an inviscid incompressible fluid is described as the geodesic flow of the right-…
Classification of Casimirs in 2D hydrodynamics
Anton Izosimov, Boris Khesin
We describe a complete list of Casimirs for 2D Euler hydrodynamics on a surface without boundary: we define generalized enstrophies which, along with circulations, form a complete…
Characterization of steady solutions to the 2D Euler equation
Anton Izosimov, Boris Khesin
Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or witho…
Coadjoint orbits of symplectic diffeomorphisms of surfaces and ideal hydrodynamics
Anton Izosimov, Boris Khesin, Mehdi Mousavi
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 Mo…