Geodesic
Vassiliev invariants and finite-dimensional approximations of the Euler equation in magnetohydrodynamics
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 161-169 
N. A. Kirin. Vassiliev invariants and finite-dimensional approximations of the Euler equation in magnetohydrodynamics. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 161-169. http://geodesic.mathdoc.fr/item/TM_2010_270_a10/
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     author = {N. A. Kirin},
     title = {Vassiliev invariants and finite-dimensional approximations of the {Euler} equation in magnetohydrodynamics},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {161--169},
     year = {2010},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_270_a10/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider Hamiltonian systems that correspond to Vassiliev invariants defined by Chen's iterated integrals of logarithmic differential forms. We show that Hamiltonian systems generated by first-order Vassiliev invariants are related to the classical problem of motion of vortices on the plane. Using second-order Vassiliev invariants, we construct perturbations of Hamiltonian systems for the classical problem of $n$ vortices on the plane. We study some dynamical properties of these systems.

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