Problèmes de linéarisation dans des familles de germes analytiques.

Abstract : We are interested in the linearization of some families of analytic germs. By generalizing definitions and properties of transfinite diameter, we obtain a polynomial majoration theorem that works both for the complex and the p-adic numbers. Then these tools are used to give a new proof of Perez-Marco's theorem about the linearization of non-resonant families of analytic germs under a polynomial perturbation. This proof allows the generalization of Perez-Marco's theorem to the p-adic case. Furthermore, with this new point of view, we obtain a diophantine information and give new examples of non linearizable germs. We generalize this theorem to the case of a perturbation with rational maps. Finally, a reasonant case is studied and we give a new proof, more elementary, of some properties of the centralizer of germs tangent to identity.
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Contributor : Dominique Vieugué <>
Submitted on : Wednesday, May 17, 2006 - 6:31:35 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
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Dominique Vieugué. Problèmes de linéarisation dans des familles de germes analytiques.. Mathématiques [math]. Université d'Orléans, 2005. Français. ⟨tel-00069473⟩

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