About the branching of real solutions of the second type in synthesis problems of radiating systems with a flat aperture

A synthesis problem of the radiating system with flat aperture by given requirements to the amplitude directivity pattern is considered. Nonuniqueness and branching of solutions depending on two real parameters and the properties of a given amplitude DP are characteristic features of this class of problems. The equation to find a set of branching points of real solutions of three types is obtained. Algorithms and examples of finding the optimal solutions are given.