Formal Poincaré-Dulac renormalization for holomorphic germs
Marco Abate Jasmin Raissy
Discrete & Continuous Dynamical Systems - A 2013, 33(5): 1773-1807 doi: 10.3934/dcds.2013.33.1773
We shall describe an alternative approach to a general renormalization procedure for formal self-maps, originally suggested by Chen-Della Dora and Wang-Zheng-Peng, giving formal normal forms simpler than the classical Poincaré-Dulac normal form. As example of application we shall compute 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-Peng). We shall also discuss a few examples of renormalization of germs tangent to the identity, revealing interesting second-order resonance phenomena.
keywords: Poincaré-Dulac normal form superattracting germs renormalization tangent to the identity maps. formal transformation

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