Contracting rigid germs in higher dimensions
[Germes rigides contractants en toute dimension]
Ruggiero, Matteo
Annales de l'Institut Fourier, Tome 63 (2013), p. 1913-1950 / Harvested from Numdam
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En suivant Favre, on dit qu’un germe holomorphe f:(ℂ d ,0)→(ℂ 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:(ℂ d ,0)→(ℂ 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.

Publié le : 2013-01-01
DOI : https://doi.org/10.5802/aif.2818
Classification:  37F25
Mots clés: germes holomorphes, point fixe, germes rigides contractants, formes normales, renormalisation, résonances, ensemble critique. 
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     author = {Ruggiero, Matteo},
     title = {Contracting rigid germs in higher dimensions},
     journal = {Annales de l'Institut Fourier},
     volume = {63},
     year = {2013},
     pages = {1913-1950},
     doi = {10.5802/aif.2818},
     zbl = {06284536},
     mrnumber = {3186512},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2013__63_5_1913_0}
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Ruggiero, Matteo. Contracting rigid germs in higher dimensions. Annales de l'Institut Fourier, Tome 63 (2013) pp. 1913-1950. doi : 10.5802/aif.2818. http://gdmltest.u-ga.fr/item/AIF_2013__63_5_1913_0/

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