  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 $\CI^2$ admitting a repulsive fixed point (by means of a family
of polunomial automorphisms composed with a Fatou-Bieberbach one). All families
will allow maximal-dimension renormalizations.
