Newton's diagram method for nonlinear equations with several small parameters

Abstract

In this article, we generalise Newton's diagram method for finding small solutions ξ(λ) of equations f (ξ,λ) = 0 (0,0) = 0 with f analytic (see [1, 2, 4, 6]) to the case of a multi-dimensional function f, unknown variable ζ and small parameter λ. This method was briefly described in [1]. The method has many different applications and allows one to solve some inflexible problems. In particular, the method can be used in very difficult bifurcation problems, for example, for systems with small imperfections.