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

Neto, Alcides Lins

doi:10.5802/aif.657

Local structural stability of

C^{2}

integrable 1-forms

Neto, Alcides Lins

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

Abstract
Résumé

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.

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.

MR 58 #2848 | Zbl 0356.58008 | 2 citations in Numdam

DOI : https://doi.org/10.5802/aif.657

@article{AIF_1977__27_2_197_0,
     author = {Neto, Alcides Lins},
     title = {Local structural stability of $C^2$ integrable 1-forms},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {27},
     number = {2},
     year = {1977},
     pages = {197-225},
     doi = {10.5802/aif.657},
     zbl = {0356.58008},
     mrnumber = {58 \#2848},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1977__27_2_197_0}
}

Neto, Alcides Lins. Local structural stability of $C^2$ integrable 1-forms. Annales de l'Institut Fourier, Volume 27 (1977) no. 2, pp. 197-225. doi : 10.5802/aif.657. http://www.numdam.org/item/AIF_1977__27_2_197_0/

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