Renormalizing Iterated Elementary Mappings and Correspondences of C

After proving a multi-dimensional extension of Zalcman's renormalization lemma and considering maximality problems about dimensions, we find renormalizing polynomial families for iterated elementary mappings, extending this result to some kinds of correspondences (by means of 'algebraic' renormalizing families) and to the family of the iterated mappings of an automorphism of ℂ admitting a repulsive fixed point (by means of a family of polunomial automorphisms composed with a Fatou-Bieberbach one). All families will allow maximaldimension renormalizations