Geodesic
Vassiliev invariants and finite-dimensional approximations of the Euler equation in magnetohydrodynamics
Informatics and Automation, Differential equations and dynamical systems, Tome 270 (2010), pp. 161-169

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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. 
@article{TRSPY_2010_270_a10,
     author = {N. A. Kirin},
     title = {Vassiliev invariants and finite-dimensional approximations of the {Euler} equation in magnetohydrodynamics},
     journal = {Informatics and Automation},
     pages = {161--169},
     publisher = {mathdoc},
     volume = {270},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_270_a10/}
}
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N. A. Kirin. Vassiliev invariants and finite-dimensional approximations of the Euler equation in magnetohydrodynamics. Informatics and Automation, Differential equations and dynamical systems, Tome 270 (2010), pp. 161-169. http://geodesic.mathdoc.fr/item/TRSPY_2010_270_a10/