The topology of integrable differential forms near a singularity

Cesar Camacho; Alcides Lins Neto

Publications Mathématiques de l'IHÉS (1982)

  • Volume: 55, page 5-35
  • ISSN: 0073-8301

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Camacho, Cesar, and Lins Neto, Alcides. "The topology of integrable differential forms near a singularity." Publications Mathématiques de l'IHÉS 55 (1982): 5-35. <http://eudml.org/doc/103982>.

@article{Camacho1982,
author = {Camacho, Cesar, Lins Neto, Alcides},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {de Rham division theorem; Frobenius theorem; Lie group action; stability of integrable forms},
language = {eng},
pages = {5-35},
publisher = {Institut des Hautes Études Scientifiques},
title = {The topology of integrable differential forms near a singularity},
url = {http://eudml.org/doc/103982},
volume = {55},
year = {1982},
}

TY - JOUR
AU - Camacho, Cesar
AU - Lins Neto, Alcides
TI - The topology of integrable differential forms near a singularity
JO - Publications Mathématiques de l'IHÉS
PY - 1982
PB - Institut des Hautes Études Scientifiques
VL - 55
SP - 5
EP - 35
LA - eng
KW - de Rham division theorem; Frobenius theorem; Lie group action; stability of integrable forms
UR - http://eudml.org/doc/103982
ER -

References

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  1. [1] C. CAMACHO, On Rk × Zl-actions, Proc. Symp. Dyn. Syst., Editor M. Peixoto, Ac. Press (1971), pp. 23-70. Zbl0274.58006MR51 #11585
  2. [2] C. CAMACHO, A. LINS NETO, Cr-structural stability of germs of integrable 1-forms, Atas do XI Colóquio Brasileiro de Matemática, vol. II (1977), pp. 565-567. 
  3. [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. Zbl0411.58018MR80j:58045
  4. [4] G. de RHAM, Sur la division des formes et des courants par une forme linéaire, Comm. Math. Helvetici, 28 (1954), pp. 346-352. Zbl0056.31601MR16,402d
  5. [5] I. KUPKA, The singularities of integrable structurally stable Pfaffian forms, Proc. Nat. Acad. Sci. U.S.A., 52 (1964), pp. 1431-1432. Zbl0137.41404MR30 #3427
  6. [6] A. LINS N., Structural stability of C2-integrable forms, Ann. Inst. Fourier, 27 (2) (1977), pp. 197-225. Zbl0351.58005
  7. [7] B. MALGRANGE, Frobenius avec singularités I. Codimension un, Publ. Math. I.H.E.S., 46 (1976), pp. 163-173. Zbl0355.32013MR58 #22685a
  8. [8] J.-F. MATTEI, R. MOUSSU, Intégrales premières d'une forme de Pfaff analytique, Ann. Inst. Fourier, 28 (4) (1978), pp. 229-347. Zbl0377.58001MR80h:58003
  9. [9] A. MEDEIROS, Structural stability of integrable differential forms, Springer Lec. Notes, 597 (1977), pp. 395-428. Zbl0363.58007MR56 #9561
  10. [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. Zbl0319.58002MR54 #3737
  11. [11] K. SAITO, Calcul algébrique de la monodromie, Astérisque 7 et 8 (1973), pp. 195-211. Zbl0294.14005MR51 #12845
  12. [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. Zbl0047.32901MR15,222b
  13. [13] S. STERNBERG, On the structure of local homeomorphisms of euclidean n-space II, Am. J. of Math., 80 (1958), pp. 623-631. Zbl0083.31406MR20 #3336
  14. [14] M. I. CAMACHO, Generic properties of homogeneous vector fields of degree two in R3, An. Acad. Bras. Ciên., 51 (1) (1979), pp. 31-33. Zbl0405.58041MR80k:58060

Citations in EuDML Documents

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  1. Jean-Paul Dufour, Aïssa Wade, Stability of higher order singular points of Poisson manifolds and Lie algebroids
  2. Jean Moulin Ollagnier, Liouvillian first integrals of homogeneouspolynomial 3-dimensional vector fields
  3. Jean-Paul Dufour, Singularities of Poisson and Nambu structures
  4. Aïssa Wade, Modèles locaux de structures de Poisson singulières en dimension 3
  5. Dominique Cerveau, Alcides Lins Neto, Formes tangentes à des actions commutatives
  6. Emmanuel Paul, Classification topologique des germes de formes logarithmiques génériques
  7. B. Azevedo Scárdua, Transversely affine and transversely projective holomorphic foliations

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