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

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.