Formal Poincare'-Dulac renormalization for holomorphic germs

Details Formal Poincare'-Dulac renormalization for holomorphic germs Formal Poincare'-Dulac renormalization for holomorphic germs

2010-08-02

arxiv.org/abs/1008.0272v2

Mathematics

Complex Variables

30 pages

Scientific paper

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.

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