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


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
Full Text: DOI Numdam EuDML


[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
[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
[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
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.