Formal Poincare'-Dulac renormalization for holomorphic germs

Abstract

In this revised version, applying a general renormalization procedure for formal self-maps, producing a formal normal form simpler than the classical Poincar\'e-Dulac normal form, we shall give a complete list of normal forms for bi-dimensional superattracting germs with non-vanishing quadratic term; in most cases, our normal forms will be the simplest possible ones (in the sense of Wang, Zheng and Peng). We shall also discuss a few examples of renormalization of germs tangent to the identity, revealing interesting second-order resonance phenomena.