A definition of a generalized filled-in Julia set generated by an infinite array of proper polynomial mappings in C N is introduced. It is shown that such Julia sets depend analytically on the defining polynomial mappings.  2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. RésuméOn introduit une définition d'un ensemble rempli de Julia généralisé qui est engendré par une matrice infinie d'applications polynomiales propres de C N . On démontre que cet ensemble de Julia dépend analytiquement des applications polynomiales définissantes.

Abstract. Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.

A compact set K ⊂ C N satisfies (ŁS) if it is polynomially convex and there exist constants B, β > 0 such thatwhere V K denotes the pluricomplex Green's function of the set K. The property was defined by Gendre and used together with the Hölder continuity of the Green's function in approximation on the set K. We construct a family of uniformly perfect totally disconnected planar attractors of iterated function systems which have the (ŁS) property.