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.