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

Neto, Alcides Lins

Local structural stability of

C^{2}

integrable 1-forms

Neto, Alcides Lins

Annales de l'Institut Fourier, Tome 27 (1977), p. 197-225 / Harvested from Numdam

Access to full text
Full (PDF)
Full (DJVU)

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.

Publié le : 1977-01-01

MR 58 #2848 | Zbl 0356.58008 | 2 citations dans 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},
     volume = {27},
     year = {1977},
     pages = {197-225},
     doi = {10.5802/aif.657},
     mrnumber = {58 \#2848},
     zbl = {0356.58008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 197-225. doi : 10.5802/aif.657. http://gdmltest.u-ga.fr/item/AIF_1977__27_2_197_0/

Bibliographie

[1] G. Reeb, Propriétés Topologiques des Variétés Feuilletées, Actualités Sci. Ind., 1183 (1952). | MR 14,1113a | Zbl 0049.12602

[2] I. Kupka, The Singularities of Integrable Structurally Stable Pfaffian Forms, Proc. of the Nat. Acad. of Sc., vol. 52 (1964), 1431. | MR 30 #3427 | Zbl 0137.41404

[3] A. S. Medeiros, Structural Stability of Integrable Differential 1-Forms, Thesis IMPA (1974), to appear. | Zbl 0363.58007

[4] C. Camacho, On Rk ˟ Zl-Actions, Proceedings of the Salvador Symposium on Dynamical Systems (1971). | Zbl 0274.58006

[5] J. Palis, On Morse-Smale Dynamical Systems, Topology, (1969). | Zbl 0189.23902

[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 21 #5794 | Zbl 0107.07102

[7] J. Sotomayor, Generic One Parameter Families of Vector Fields on Two-Dimensional Manifolds, Publ. Math. 43, IHESc. | Numdam | Zbl 0279.58008

[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 42 #6872 | Zbl 0215.53001

[9] P. Hartman, Ordinary Differential Equations, edited by John Wiley and Sons Inc., 1964. | MR 30 #1270 | Zbl 0125.32102

[10] C. Camacho, Structural Stability of integrable forms on 3-manifolds, to appear. | Zbl 0391.58013