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

Dans ce travail, on considère une classe de germes de singularités de 1-formes intégrables dans R n qui sont C r structuralement stables (r2 si n=3, r4 si n4). 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 (r2 if n=3, r4 if n4), whose 1-jet is zero at the singularity. In this class the stability depends essentially on the fact that the perturbations allowed are integrable.

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     author = {Neto, Alcides Lins},
     title = {Local structural stability of $C^2$ integrable 1-forms},
     journal = {Annales de l'Institut Fourier},
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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://www.numdam.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

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