no. 2
Local structural stability of C 2 integrable 1-forms
Annales de l'Institut Fourier, Volume 27 (1977) no. 2, pp. 197-225.

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≥2 if n=3, r≥4 if n≥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≥2 si n=3, r≥4 si n≥4). Dans cette classe la stabilité dépend essentiellement de ce que les perturbations permises sont intégrables.

@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},
     zbl = {0356.58008},
     mrnumber = {58 #2848},
     language = {en},
     url = {https://aif.centre-mersenne.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  - https://aif.centre-mersenne.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 https://aif.centre-mersenne.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, Volume 27 (1977) no. 2, pp. 197-225. doi : 10.5802/aif.657. https://aif.centre-mersenne.org/articles/10.5802/aif.657/

[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

Cited by Sources: