Have a personal or library account? Click to login
Characterization of second type plane foliations using Newton polygons Cover

References

  1. [Br] M. Brunella. Some Remarks on Indices of Holomorphic Vector Fields. Publicacions Matemàtiques, Vol 41. (1997), 527-544.10.5565/PUBLMAT_41297_17
  2. [Cam-Li-Sad] C. Camacho, A. Lins Neto and P. Sad. Topological Invariants and Equidesigularisation for Holomorphic Vector Fields. J. Differential Geometry, 20, (1984), pp. 143-174.
  3. [Cam-Sad1] C. Camacho and P. Sad. Pontos Singulares de Ecuações Diferenciais Analíticas. 16 Coloquio Brasileiro de Matemática, IMPA.(1987).
  4. [Cam-Sad2] C. Camacho and P. Sad. Invariant varieties through singularities of holomorphic vector fields. Ann. of Math. (1982), 579-595.10.2307/2007013
  5. [Can-Co-Mol] F. Cano, N. Corral and R. Mol. Local polar invariants for plane singular foliations. Expo. Math. 37 (2019), no. 2, 145-164.
  6. [Cav-Le] V. Cavalier - D. Lehmann. Localisation des résidus de Baum-Bott, courbes généralisées et K-théorie. I. Feuilletages dans C2. Compos. Math. Helv. 76 (2001), no. 4, 665-668.10.1007/s00014-001-8324-9
  7. [Ce-Mou] D. Cerveau and R. Moussu. Groupes d’automorphismes de (ℂ, 0) et équations différentielles ydy + … = 0, Bull. Soc. Math. France 116 (1988) 459-488.10.24033/bsmf.2108
  8. [Co] N. Corral. Curvas polares de una foliación singular. Tesis Doctoral. Universidad de Valladolid, (2001).
  9. [Du] H. Dulac. Recherches sur les points singuliers des équations différentielles. Thèse.
  10. [F-Moz-N] P. Fernández - J. Mozo - H. Neciosup. On codimension one foliations with prescribed cuspidal separatriz. J. Differential Equations 256 (2014), 1702-1717.10.1016/j.jde.2013.12.002
  11. [FP-Mol] A. Fernández Pérez - R. Mol. Residue-Type indices and Holomorphic Foliations. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19 (2019), no. 3, 1111-1134.10.2422/2036-2145.201703_006
  12. [GB] E. R. García Barroso. Invariants des singularités de courbes planes et courbure des fibres de Milnor. Thèse, École Normale Supérieure, LMENS-96-35, 1996.
  13. [GB-Gw] E. R. García Barroso-J. Gwoździewicz. On the approximate Jacobian Newton diagrams of an irreducible plane curve. J. Math. Soc. Japan (2013), Vol. 65, (1), 169-182.10.2969/jmsj/06510169
  14. [Ge-Mol] Y. Genzmer-R. Mol. Local polar invariants and the Poincaré problem in the dicritical case. J. Math. Soc. Japan 70 (2018), no. 4, 1419-1451.10.2969/jmsj/76227622
  15. [Go-Sea-Ve] X. Gómez - J. Seade - A. Verjovsky. The index of a holomorphic flow with an isolated singularity. Math. Ann. 291 (1991), 737-751.10.1007/BF01445237
  16. [Lo] F. Loray. Réduction formelle des singularités cuspidales de champs de vecteurs analytiques. J. Differential Equations 158 (1999), 152-173.10.1016/S0022-0396(99)80021-7
  17. [Ma-Mou] J.-F. Mattei, R. Moussu. Holonomie et intégrales premiéres. Ann. Sci. École Norm. Sup. (4). 13 (1980), no. 4, 469-523.
  18. [Ma-Sal] J.-F. Mattei, E. Salem. Modules formels locaux de feuilletages holomorphes. arXiv:math/0402256 (2004).
  19. [Mer] M. Merle. Invariants polaires des courbes planes. Invent. Math. 41, (1997), 103-111.10.1007/BF01418370
  20. [Mez] R. Meziani. Probleme de module pour des equations differentielles dégénérées de (ℂ2, 0). Tesis Doctoral. Université de Rennes I (1992).
  21. [R] P. Rouillé. Théoréme de Merle: cas des 1-formes de type courbes généralisées. Bol. Soc. Mat. (1999). Vol. 30, (3), 293-314.10.1007/BF01239008
  22. [Sar] N. Saravia. Curva polar de una foliación asociada a sus raíces aproximadas. Tesis Doctoral. Pontificia Universidad Católica del Perú, (2018).
  23. [Sei] A. Seidenberg. Reduction of Singularities of the Differentiable Equation A dY = B dX. Amer. Journal of Math. 90, (1968), P. 248-269.10.2307/2373435
  24. [St] E. Strózyna. The analytic and formal normal form for the nilpotent singulatity. The case of case generalized saddle-node Bull. Sci. Math. 126 (2002), 555-579.10.1016/S0007-4497(02)01127-2
  25. [Ta] F. Takens. Singularities of vectors fields. Inst. Hautes Études Sci. Publ. Math. 43 (1974) 47-100.10.1007/BF02684366
DOI: https://doi.org/10.2478/auom-2022-0021 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 103 - 123
Submitted on: Jul 6, 2021
|
Accepted on: Sep 30, 2021
|
Published on: Jun 2, 2022
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2022 Percy Fernández-Sánchez, Evelia R. García barroso, Nancy Saravia-Molina, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.