no. 5
Contracting rigid germs in higher dimensions
Ruggiero, Matteo1
1Fondation Mathématique Jacques Hadamard, Département de Mathématiques, UMR 8628 Université Paris-Sud 11-CNRS, Bâtiment 425, Faculté des Sciences d’Orsay, Université Paris-Sud 11, F-91405 Orsay Cedex, France. Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128 Palaiseau Cedex, France.
Annales de l'Institut Fourier, Volume 63 (2013) no. 5, pp. 1913-1950

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.

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.

DOI: 10.5802/aif.2818
Classification: 37F25
Keywords: holomorphic fixed point germs, contracting rigid germs, normal forms, renormalization, resonances, critical set.
Mots-clés : germes holomorphes, point fixe, germes rigides contractants, formes normales, renormalisation, résonances, ensemble critique.

Ruggiero, Matteo  1

1 Fondation Mathématique Jacques Hadamard, Département de Mathématiques, UMR 8628 Université Paris-Sud 11-CNRS, Bâtiment 425, Faculté des Sciences d’Orsay, Université Paris-Sud 11, F-91405 Orsay Cedex, France. Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128 Palaiseau Cedex, France. 
Ruggiero, Matteo. Contracting rigid germs in higher dimensions. Annales de l'Institut Fourier, Volume 63 (2013) no. 5, pp. 1913-1950. doi: 10.5802/aif.2818
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