On the structure of the set of self-similar quadruples of point vortices in the plane

It has been shown that the set of self-similar configurations of point vortices in the plane is the set of zeros of a vector field. A numerical procedure for seeking the zeros has been proposed. By using this procedure, for the circulation used by Novikov, new components of the set of self-similar configurations of fours vortices, different from the ellipse identified by Novikov, have been found numerically.