Discrete-time Point Vortex Dynamics

The paper examines a difference equation, analogous to the Helmholtz equation, which describes the point vortex dynamics on a plane under control. The dependence of the asymptotic behaviour of the moment of vorticity of a system of point vortices on the control parameters is established. In the presence of random perturbations, for a system of point vortices the parameter estimation problem is solved. An optimal control allowing the maintenance of two point vortices on a specified rotational orbit under minor changes in the initial control parameters has been found.