Ruggiero, Matteo
Contracting rigid germs in higher dimensions  [ Germes rigides contractants en toute dimension ]
Annales de l'institut Fourier, Tome 63 (2013) no. 5 , p. 1913-1950
MR 3186512 | Zbl 06284536
doi : 10.5802/aif.2818
URL stable : http://www.numdam.org/item?id=AIF_2013__63_5_1913_0

Classification:  37F25
Mots clés: germes holomorphes, point fixe, germes rigides contractants, formes normales, renormalisation, résonances, ensemble critique.
En suivant Favre, on dit qu’un germe holomorphe f:( d ,0)( d ,0) est rigide si l’union de l’ensemble critique de tous ses itérés est à croisement normaux. Nous donnons une classification partielle des germes rigides contractants en toute dimension à conjugaison holomorphe près. On trouve des nouveaux phénomènes de résonance, entre la différentielle de f et son action linéaire sur le groupe fondamental du complémentaire de l’ensemble critique.
Following Favre, we define a holomorphic germ f:( d ,0)( d ,0) to be rigid if the union of the critical set of all iterates has simple normal crossing singularities. We give a partial classification of contracting rigid germs in arbitrary dimensions up to holomorphic conjugacy. Interestingly enough, we find new resonance phenomena involving the differential of f and its linear action on the fundamental group of the complement of the critical set.

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