Renormalizing iterated elementary mappings and correspondences of C^2
Complex Variables
2008-06-16 v2
Abstract
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 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.
Cite
@article{arxiv.math/0211381,
title = {Renormalizing iterated elementary mappings and correspondences of C^2},
author = {Claudio Meneghini},
journal= {arXiv preprint arXiv:math/0211381},
year = {2008}
}