Local structural stability of $C^2$ integrable 1-forms

Lins Neto, Alcides

doi:10.5802/aif.657

Local structural stability of

C^{2}

integrable 1-forms

Lins Neto, Alcides

Annales de l'Institut Fourier, Tome 27 (1977) no. 2, pp. 197-225.

Résumé
Abstract

Dans ce travail, on considère une classe de germes de singularités de 1-formes intégrables dans $R^{n}$ qui sont $C^{r}$ structuralement stables ( $r \geq 2$ si $n = 3$ , $r \geq 4$ si $n \geq 4$ ). Dans cette classe la stabilité dépend essentiellement de ce que les perturbations permises sont intégrables.

In this work we consider a class of germs of singularities of integrable 1-forms in $R^{n}$ which are structurally stable in class $C^{r}$ ( $r \geq 2$ if $n = 3$ , $r \geq 4$ if $n \geq 4$ ), whose 1-jet is zero at the singularity. In this class the stability depends essentially on the fact that the perturbations allowed are integrable.

MR Zbl | 3 citations dans Numdam

DOI : 10.5802/aif.657

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     title = {Local structural stability of $C^2$ integrable 1-forms},
     journal = {Annales de l'Institut Fourier},
     pages = {197--225},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {27},
     number = {2},
     year = {1977},
     doi = {10.5802/aif.657},
     mrnumber = {58 #2848},
     zbl = {0356.58008},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.657/}
}

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Lins Neto, Alcides . Local structural stability of $C^2$ integrable 1-forms. Annales de l'Institut Fourier, Tome 27 (1977) no. 2, pp. 197-225. doi : 10.5802/aif.657. http://archive.numdam.org/articles/10.5802/aif.657/

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