no. 5
Integrable analytic vector fields with a nilpotent linear part
Annales de l'Institut Fourier, Tome 45 (1995) no. 5, pp. 1449-1470.

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.

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.

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     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},
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Gong, Xianghong. Integrable analytic vector fields with a nilpotent linear part. Annales de l'Institut Fourier, Tome 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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