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Javier Ribón
Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy
(Non-existence de plongements de difféomorphismes unipotents à conjugaison formelle près)
Annales de l'institut Fourier, 59 no. 3 (2009), p. 951-975, doi: 10.5802/aif.2453
Article: subscription required (your ip address: 174.129.163.183) | Reviews MR 2543658 | Zbl 1186.37057
Class. Math.: 37F75, 32H02, 32A05, 40A05
Keywords: Holomorphic dynamical systems, diffeomorphisms, vector fields, potential theory

Résumé - Abstract

The formal class of a germ of diffeomorphism $\varphi $ is embeddable in a flow if $\varphi $ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at $\mathbb{C}^{n}$ ($n>1$) 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.

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