Formal Poincare'-Dulac renormalization for holomorphic germs

2010/08/02 by Abate, Marco, Raissy, Jasmin
#32H50 #37F99 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1008.0272

Abstract

In this revised version, applying a general renormalization procedure for formal self-maps, producing a formal normal form simpler than the classical Poincaré-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.

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