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Vassiliev invariants and finite-dimensional approximations of the euler equation in magnetohydrodynamics

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Abstract

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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Authors and Affiliations

  1. Moscow State Regional Institute for the Social Science and Humanities (Kolomna State Pedagogical Institute), Zelenaya ul. 30, Kolomna, Moscow oblast, 140411, Russia

    N. A. Kirin

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  1. N. A. Kirin
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Correspondence to N. A. Kirin.

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Original Russian Text © N.A. Kirin, 2010, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Vol. 270, pp. 161–169.

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Kirin, N.A. Vassiliev invariants and finite-dimensional approximations of the euler equation in magnetohydrodynamics. Proc. Steklov Inst. Math. 270, 156–164 (2010). https://doi.org/10.1134/S0081543810030119

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  • DOI: https://doi.org/10.1134/S0081543810030119

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