Iterations, Interlaced Equations, and Lyapunov Convex Majorants in Nonlinear Analysis

The geometry of Newton diagrams and polyhedrons (see Bruno [1], Vainberg and Trenogin [1, 2]) provides a major function in the branching theory. Recently these geometric constructions have been used to the finding of branching solutions by the iteration methods (see Sidorov [23, 24]).