Contracting rigid germs in higher dimensions
[Germes rigides contractants en toute dimension]
Annales de l'Institut Fourier, Tome 63 (2013) no. 5, pp. 1913-1950.

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.

DOI : 10.5802/aif.2818
Classification : 37F25
Keywords: holomorphic fixed point germs, contracting rigid germs, normal forms, renormalization, resonances, critical set.
Mot 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.
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Ruggiero, Matteo. Contracting rigid germs in higher dimensions. Annales de l'Institut Fourier, Tome 63 (2013) no. 5, pp. 1913-1950. doi : 10.5802/aif.2818. http://www.numdam.org/articles/10.5802/aif.2818/

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