Modèles locaux de champs et de formes

Roussarie, Robert

Astérisque, no. 30 (1975) , 183 p.

Résumé

In this paper, we obtain some results of finite determination for vector fields and 2-closed forms, (Finite determinated vector fields or forms admit polynomial models). The whole paper is based on a study of certain singular differential equations such that where $X$ is a singular vector field. The most important results concerning vector fields are obtained for germs in the plane. We give conditions under which formal equivalence or existence of formal integral implie $C^{\infty}$ -equivalence or existence of $C^{\infty}$ integral. For démonstrations, we use the "blowing up" method and some other results of F. Takens and F. Dumortier. We also study germs of 2-closed forms in and show that all the germs of codimension less than 3 are stable.

MR Zbl | 15 citations dans Numdam

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     year = {1975},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {30},
     mrnumber = {440570},
     zbl = {0327.57017},
     language = {fr},
     url = {https://www.numdam.org/item/AST_1975__30__1_0/}
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Roussarie, Robert. Modèles locaux de champs et de formes. Astérisque, no. 30 (1975), 183 p. https://www.numdam.org/item/AST_1975__30__1_0/

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