ANZIAM  J.  44 (2002), 247-259
Newton's diagram method for nonlinear equations with several small parameters

Peter Aizengendler
  Professor Peter Aizengendler, late of Pscov University, Russia, died in November 2000.
  This paper, his last mathematical testament, is published with the kind consent of his son,
  Dr Mark Aizengendler, 11 Varram Way, West Lakes Shore, SA 5020, Australia.
    mark_15jan@yahoo.com.au


Abstract
In this article, we generalise Newton's diagram method for finding small solutions $\xi(\lambda)$ of equations $f(\xi, \lambda)=0$ ($f(0,0)=0$) with $f$ analytic (see [1, 2, 4, 6]) to the case of a multi-dimensional function $f$, unknown variable $\xi$ and small parameter $\lambda$. 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.
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