GROUP SYMMETRY OF THE LYAPUNOV-SCHMIDT BRANCHING EQUATION AND ITERATIVE METHODS IN THE PROBLEM OF A BIFURCATION POINT

Abstract

Using group-theoretic methods (MR 80d: 58072, 83m: 58082), the authors construct the general form of the branching equation, symmetric with respect to fundamental representations of the rotation group, and on the basis of this form they propose an iterative method for calculating families of small branching solutions in a neighborhood of a bifurcation point, depending on free parameters.