Configurations of zeroes of analytic functions

Abstract

The paper deals with analytic families of functions (f(lambda))(lambda) with f(lambda0) equivalent to 0. We want to investigate what kind of configurations of zeroes can arise from a given non-isolated zero of f(lambda), with lambda close to lambda (0). This investigation can be reduced to the study of all I-parameter subfamilies, which are induced from (f(lambda))(lambda) by analytic curves through lambda (0). Finally, we give an application of this result in the theory of dynamical systems. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.