Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Journals Home Search My Subscriptions Subscribe
Previous issue | This issue | Most recent issue | All issues (1900–Present) | Next issue | Previous article | Articles in press | Recently published articles | Next article
Request Permissions
 
 

 

Semi-complete vector fields of saddle-node type in $ \mathbb{C}^n$


Author: Helena Reis
Journal: Trans. Amer. Math. Soc. 360 (2008), 6611-6630
MSC (2000): Primary 32S65
DOI: https://doi.org/10.1090/S0002-9947-08-04516-9
Published electronically: July 24, 2008
MathSciNet review: 2434302
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We classify the foliations associated to codimension $ 1$ saddle-node vector fields on $ \mathbb{C}^n$, with an isolated singularity, admitting a semi-complete representative. This will be done under some further assumptions that are generic in dimension $ 3$. These singularities play an essential role in the program to classify semi-complete vector fields in dimension $ 3$.

References [Enhancements On Off] (What's this?)

  • 1. J. C. Canille Martins, Contribuição ao estudo local de fluxos holomorfos com ressonância, Ph.D. Thesis, IMPA-CNPq, Brasil (1985)
  • 2. J. C. Canille Martins, Comportement qualitatif des systèmes symétriques, Comptes Rendus de l'Académie des Sciences de Paris, t-301, ser. II, n. 10 (l985)
  • 3. E. Ghys, J. Rebelo, Singularités des flots holomorphes II, Ann. Inst. Fourrier, Vol. 47, No. 4 (1997), 1117-1174 MR 1488247 (99a:32059)
  • 4. J. Malmquist, Sur l'étude analytique des solutions d'un système d'équations dans le voisinage d'un point de indetermination, Acta Math. 73 (1941), 87-129 MR 0003897 (2:289c)
  • 5. B. Malgrange, Remarques sur les équations différentielles à points singuliers irréguliers, Lectures Notes No. 712, Springer, (1979), 77-86 MR 548145 (80k:14019)
  • 6. J. Martinet, J.P. Ramis, Problèmes de modules pour des équations différentielles non linéaires du premier ordre, Publ. Math. I.H.E.S., 55 (1982), 63-164 MR 672182 (84k:34011)
  • 7. J. Rebelo, Singularités des flots holomorphes, Ann. Inst. Fourrier, Vol. 46, No. 2 (1996), 411-428 MR 1393520 (97d:32059)
  • 8. J. Rebelo, Réalisation de germes de feuilletages holomorphes par des champs semi-complets en dimension $ 2$, Ann. Fac. Sci. Toulouse, Vol. 9, No. 4 (2000), 735-763 MR 1838147 (2002e:32044)
  • 9. J. Rebelo, Complete algebraic vector fields on affine surfaces, part I, The Journal of Geometric Analysis, Vol. 13, No. 4 (2003), 669-696 MR 2005159 (2005b:32050)
  • 10. H. Reis, Analytic classification of complex differential equations, Ph.D. Thesis, Univ. Porto (2006).
  • 11. L. Stolovitch, Classification analytique de champs de vecteurs $ 1$-résonnants de $ (\mathbb{C}^n,0)$, Asymptotic Anal. Vol. 12, No. 2 (1996), 91-143. MR 1386227 (98b:32037)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 32S65

Retrieve articles in all journals with MSC (2000): 32S65

Additional Information

Helena Reis
Affiliation: Centro de Matemática da Universidade do Porto, Faculdade de Economia da Universidade do Porto, Porto, Portugal
Email: hreis@fep.up.pt

DOI: https://doi.org/10.1090/S0002-9947-08-04516-9
Received by editor(s): March 16, 2005
Received by editor(s) in revised form: March 5, 2007
Published electronically: July 24, 2008
Additional Notes: The author received financial support from Fundação para a Ciência e Tecnologia (FCT) through Centro de Matemática da Universidade do Porto, and from PRODEPIII
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society