Formal normal forms for holomorphic maps tangent to the identity
Marco Abate Francesca Tovena
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.
keywords: Maps tangent to the identity formal normal forms.
Formal Poincaré-Dulac renormalization for holomorphic germs
Marco Abate Jasmin Raissy
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

Year of publication

Related Authors

Related Keywords

[Back to Top]