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Camacho, Cesar; Lins Neto, Alcidés

The topology on integrable differential forms near a singularity. (English) Zbl 0505.58026

Publ. Math., Inst. Hautes Étud. Sci. 55, 5-35 (1982).
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Cited in 24 Documents

MSC:

37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
58A10 Differential forms in global analysis
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory

Keywords:

de Rham division theorem; Frobenius theorem; Lie group action; stability of integrable forms
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References:

[1] C. Camacho, On Rk {\(\times\)} Zl-actions,Proc. Symp. Dyn. Syst., Editor M. Peixoto, Ac. Press (1971), pp. 23–70.
[2] C. Camacho, A. Lins Neto, C r -structural stability of germs of integrable 1-forms,Atas do XI Colóquio Brasileiro de Matemática, vol. II (1977), pp. 565–567.
[3] C. Camacho, N. Kuiper, J. Palis, The topology of holomorphic flows with singularity,Publ. Math. I.H.E.S.,48 (1978), pp. 5–38. · Zbl 0411.58018
[4] G. de Rham, Sur la division des formes et des courants par une forme linéaire,Comm. Math. Helvetici,28 (1954), pp. 346–352. · Zbl 0056.31601 · doi:10.1007/BF02566941
[5] I. Kupka, The singularities of integrable structurally stable Pfaffian forms,Proc. Nat. Acad. Sci. U.S.A.,52 (1964), pp. 1431–1432. · Zbl 0137.41404 · doi:10.1073/pnas.52.6.1431
[6] A. Lins N., Structural stability of C2-integrable forms,Ann. Inst. Fourier,27 (2) (1977), pp. 197–225. · Zbl 0356.58008
[7] B. Malgrange, Frobenius avec singularités I. Codimension un,Publ. Math. I.H.E.S.,46 (1976), pp. 163–173. · Zbl 0355.32013
[8] J.-F. Mattei, R. Moussu, Intégrales premières d’une forme de Pfaff analytique,Ann. Inst. Fourier,28 (4) (1978), pp. 229–347.
[9] A. Medeiros, Structural stability of integrable differential forms,Springer Lec. Notes,597 (1977), pp. 395–428. · Zbl 0363.58007
[10] R. Moussu, Sur l’existence d’intégrales premières pour un germe de forme de Pfaff,Ann. Inst. Fourier,26 (2) (1976), pp. 171–220. · Zbl 0319.58002
[11] K. Saito, Calcul algébrique de la monodromie,Astérisque 7 et 8 (1973), pp. 195–211. · Zbl 0294.14005
[12] C. L. Siegel, Über die normalform analytischer differentialgleichungen in der nähe einer Gleichgewichtslösung,Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl. (1952), pp. 21–30. · Zbl 0047.32901
[13] S. Sternberg, On the structure of local homeomorphisms of euclideann-space II,Am. J. of Math.,80 (1958), pp. 623–631. · Zbl 0083.31406 · doi:10.2307/2372774
[14] M. I. Camacho, Generic properties of homogeneous vector fields of degree two inR 3,An. Acad. Bras. Ciên.,51 (1) (1979), pp. 31–33. · Zbl 0405.58041
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