Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy
[Non-existence de plongements de difféomorphismes unipotents à conjugaison formelle près]
Ribón, Javier
Annales de l'Institut Fourier, Tome 59 (2009), p. 951-975 / Harvested from Numdam
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La classe formelle d’un difféomorphisme local ϕ est plongeable dans un flot si ϕ est formellement conjugué à l’exponentielle d’un germe de champs de vecteurs. On prouve qu’il existe des difféomorphismes unipotents analytiques complexes définis au voisinage de l’origine dans ℂ n (n>1) dont la classe formelle n’est pas plongeable. Les exemples appartiennent à une famille où le manque de plongeabilité est une propriété de type géométrique. La preuve est basée sur les propriétés de certains opérateurs fonctionnels linéaires qu’on obtient grâce à l’étude des familles polynomiales de difféomorphismes via la théorie du potentiel.

The formal class of a germ of diffeomorphism ϕ is embeddable in a flow if ϕ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at ℂ n (n>1) whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms via potential theory.

Publié le : 2009-01-01
DOI : https://doi.org/10.5802/aif.2453
Classification:  37F75,  32H02,  32A05,  40A05
Mots clés: systèmes dynamiques holomorphes, difféomorphismes, champs de vecteurs, théorie du potentiel 
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     title = {Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy},
     journal = {Annales de l'Institut Fourier},
     volume = {59},
     year = {2009},
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     doi = {10.5802/aif.2453},
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     mrnumber = {2543658},
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Ribón, Javier. Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy. Annales de l'Institut Fourier, Tome 59 (2009) pp. 951-975. doi : 10.5802/aif.2453. http://gdmltest.u-ga.fr/item/AIF_2009__59_3_951_0/

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