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, 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

@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},
     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/}
}

TY  - JOUR
AU  - Neto, Alcides Lins
TI  - Local structural stability of $C^2$ integrable 1-forms
JO  - Annales de l'Institut Fourier
PY  - 1977
SP  - 197
EP  - 225
VL  - 27
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/articles/10.5802/aif.657/
DO  - 10.5802/aif.657
LA  - en
ID  - AIF_1977__27_2_197_0
ER  -

%0 Journal Article
%A Neto, Alcides Lins
%T Local structural stability of $C^2$ integrable 1-forms
%J Annales de l'Institut Fourier
%D 1977
%P 197-225
%V 27
%N 2
%I Institut Fourier
%C Grenoble
%U http://archive.numdam.org/articles/10.5802/aif.657/
%R 10.5802/aif.657
%G en
%F AIF_1977__27_2_197_0

Neto, Alcides Lins. 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/

Bibliographie
Cité par

[1] G. Reeb, Propriétés Topologiques des Variétés Feuilletées, Actualités Sci. Ind., 1183 (1952). | MR | Zbl

[2] I. Kupka, The Singularities of Integrable Structurally Stable Pfaffian Forms, Proc. of the Nat. Acad. of Sc., vol. 52 (1964), 1431. | MR | Zbl

[3] A. S. Medeiros, Structural Stability of Integrable Differential 1-Forms, Thesis IMPA (1974), to appear. | Zbl

[4] C. Camacho, On Rk ˟ Zl-Actions, Proceedings of the Salvador Symposium on Dynamical Systems (1971). | Zbl

[5] J. Palis, On Morse-Smale Dynamical Systems, Topology, (1969). | Zbl

[6] M. C. Peixoto and M. Peixoto, Structural Stability in the Plane with Enlarged Boundary Conditions, Ann. Acad. Bras. Sci., vol. 81 (1959), 135-160. | MR | Zbl

[7] J. Sotomayor, Generic One Parameter Families of Vector Fields on Two-Dimensional Manifolds, Publ. Math. 43, IHESc. | Numdam | Zbl

[8] M. W. Hirsch and C. C. Pugh, Stable Manifolds and Hyperbolic Sets, Global Analysis, Proc. Symp. in Pure Math., vol. XIV, AMS (1970). | MR | Zbl

[9] P. Hartman, Ordinary Differential Equations, edited by John Wiley and Sons Inc., 1964. | MR | Zbl

[10] C. Camacho, Structural Stability of integrable forms on 3-manifolds, to appear. | Zbl

Cité par Sources :