We study the normalization of analytic vector fields with a nilpotent linear part. We prove that such an analytic vector field can be transformed into a certain form by convergent transformations when it has a non-singular formal integral. We then prove that there are smoothly linearizable parabolic analytic transformations which cannot be embedded into the flows of any analytic vector fields with a nilpotent linear part.
On étudie la normalisation des champs de vecteurs analytiques à partie linéaire nilpotente. On démontre qu’un tel champ de vecteurs analytique peut être transformé en une certaine forme par des transformations convergentes s’il a une intégrale formelle non singulière. Alors on montre qu’il existe des applications analytiques paraboliques différentiablement linéarisables qui ne peuvent être plongées dans le flot d’aucun champ de vecteurs analytique avec une partie linéaire nilpotente.
@article{AIF_1995__45_5_1449_0, author = {Gong, Xianghong}, title = {Integrable analytic vector fields with a nilpotent linear part}, journal = {Annales de l'Institut Fourier}, pages = {1449--1470}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {45}, number = {5}, year = {1995}, doi = {10.5802/aif.1502}, mrnumber = {96m:58229}, zbl = {0835.58032}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1502/} }
TY - JOUR AU - Gong, Xianghong TI - Integrable analytic vector fields with a nilpotent linear part JO - Annales de l'Institut Fourier PY - 1995 SP - 1449 EP - 1470 VL - 45 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1502/ DO - 10.5802/aif.1502 LA - en ID - AIF_1995__45_5_1449_0 ER -
%0 Journal Article %A Gong, Xianghong %T Integrable analytic vector fields with a nilpotent linear part %J Annales de l'Institut Fourier %D 1995 %P 1449-1470 %V 45 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1502/ %R 10.5802/aif.1502 %G en %F AIF_1995__45_5_1449_0
Gong, Xianghong. Integrable analytic vector fields with a nilpotent linear part. Annales de l'Institut Fourier, Volume 45 (1995) no. 5, pp. 1449-1470. doi : 10.5802/aif.1502. http://archive.numdam.org/articles/10.5802/aif.1502/
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