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PROC

We describe a procedure for constructing formal normal forms of holomorphic maps with a hypersurface of mixed points, and we apply it to obtain a complete
list of formal normal forms for 2-dimensional holomorphic maps tangential to a curve
of mixed points.

DCDS

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.

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