The topology of holomorphic flows with singularity

Cesar Camacho; Nicolaas H. Kuiper; Jacob Palis

Publications Mathématiques de l'IHÉS (1978)

  • Volume: 48, page 5-38
  • ISSN: 0073-8301

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Camacho, Cesar, Kuiper, Nicolaas H., and Palis, Jacob. "The topology of holomorphic flows with singularity." Publications Mathématiques de l'IHÉS 48 (1978): 5-38. <http://eudml.org/doc/103956>.

@article{Camacho1978,
author = {Camacho, Cesar, Kuiper, Nicolaas H., Palis, Jacob},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {holomorphic flows with singularity; topological conjugacy; Siegel domain; Poincare domain; singular foliations},
language = {eng},
pages = {5-38},
publisher = {Institut des Hautes Études Scientifiques},
title = {The topology of holomorphic flows with singularity},
url = {http://eudml.org/doc/103956},
volume = {48},
year = {1978},
}

TY - JOUR
AU - Camacho, Cesar
AU - Kuiper, Nicolaas H.
AU - Palis, Jacob
TI - The topology of holomorphic flows with singularity
JO - Publications Mathématiques de l'IHÉS
PY - 1978
PB - Institut des Hautes Études Scientifiques
VL - 48
SP - 5
EP - 38
LA - eng
KW - holomorphic flows with singularity; topological conjugacy; Siegel domain; Poincare domain; singular foliations
UR - http://eudml.org/doc/103956
ER -

References

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  1. [1] A. D. BRJUNO, Analytical form of differential equations, Trudy Moscow Math. Obšč (Trans. Moscow Math. Soc.), vol. 25 (1971), p. 131-288. Zbl0272.34018MR51 #13365
  2. [2] C. CAMACHO, N. H. KUIPER, J. PALIS, La topologie du feuilletage d'un champ de vecteurs holomorphe près d'une singularité, C.R. Acad. Sc. Paris, t. 282 A, p. 959-961. Zbl0353.32015MR54 #1301
  3. [3] Topological properties of R2-actions are studied in : C. CAMACHO, On Rk x Zl-actions, Proceed. Symp. on Dynamical Systems, Salvador 1971, Ed. Peixoto, p. 23-70. G. PALIS, Linearly induced vector fields and R2-actions on spheres, to appear in J. Diff. Geom. C. CAMACHO, Structural stability theorems for integrable differential forms on 3-manifolds, to appear in Topology. 
  4. [4] H. DULAC, Solutions d'un système d'équations différentielles dans le voisinage des valeurs singulières, Bull. Soc. Math. France, 40 (1912), 324-383. Zbl43.0391.01JFM43.0391.01
  5. [5] J. GUCKENHEIMER, Hartman's theorem for complex flows in the Poincaré domain, Composito Math., 24 (1972), p. 75-82. Zbl0239.58007MR46 #920
  6. [6] A real analogue of theorem III is the classical Grobman-Hartman theorem : P. HARTMAN, Proc. AMS, 11 (1960), p. 610-620. MR22 #12279
  7. [7] Topological properties of real linear flows on Rn are studied in : N. H. KUIPER, Manifolds Tokyo, Proceedings Int. Conference, Math. Soc. Japan (1973), p. 195-204, and : N. N. LADIS, Differentialnye Uraunenya Volg. (1973), p. 1222-1235. 
  8. [8] D. LIEBERMAN, Holomorphic vector fields on projective varieties, Proc. Symp. Pure Math., XXX (1976), 273-276. Zbl0365.32021MR56 #12337
  9. [9] The invariant of chapter I goes back to an invariant in the study of stability in one parameter families of diffeomorphisms : S. NEWHOUSE, J. PALIS, F. TAKENS, to appear. See also : J. PALIS, A differentiable invariant of topological conjugacies and moduli of stability, preprint IMPA. 
  10. [10] J. PALIS, S. SMALE, Structural stability theorems, Global Analysis, Symp. Pure Math., AMS, vol. XIV (1970), p. 223-231. Zbl0214.50702MR42 #2505
  11. [11] H. POINCARÉ, Sur les propriétés des fonctions définies par les équations aux différences partielles, thèse, Paris, 1879 = Œuvres complètes, I, p. XCIX-CV. 
  12. [12] H. RUSSMANN, On the convergence of power series transformations of analytic mappings near a fized point into a normal form, Bures-sur-Yvette, preprint I.H.E.S. 
  13. [13] C. L. SIEGEL, Über die Normalform analytischer Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Göttingen, Nachr. Akad. Wiss., Math. Phys. Kl. (1952), p. 21-30. Zbl0047.32901MR15,222b
  14. [14] C. L. SIEGEL, J. MOSER, Celestial mechanics (1971) (English edition of : C. L. SIEGEL, Vorlesungen über Himmelsmechanik, 1954, Springer Verlag). 
  15. [15] С. Ильяшенко, ӠАМЕЧАНИЯ О ТОПОЛОГИИ ОСОБЬIX ТОЧЕК АНАЛИТИЧЕСКИX ДИФФЕРЕ-НЦИАЛЬНЬIX уРАВНЕНИЙ В КОМПЛЕКСНОЙ ОБЛАСТИ И ТЕОРЕМА ЛАДИСА, Функuuональныŭ аналuƏ u еゞо nрuломенuя T. II, ВЬIН 2, 1977, 28-38. 
  16. [16] J. GUCKENHEIMER, On holomorphic vector fields on CP(2), An. Acad. Brasil. Cienc., 42 (1970), p. 415-420. Zbl0205.54101MR44 #2254
  17. [17] F. DUMORTIER, R. ROUSSARIE, Smooth linearization of germs of R2-actions and holomorphic vector fields, to appear. Zbl0418.58015

Citations in EuDML Documents

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  1. Jean Martinet, Normalisation des champs de vecteurs holomorphes
  2. Dominique Cerveau, Densité des feuilles de certaines équations de Pfaff à 2 variables
  3. Sylvain E. Cappell, Julius L. Shaneson, The topological rationality of linear representations
  4. Cesar Camacho, Alcides Lins Neto, The topology of integrable differential forms near a singularity
  5. Marc Chaperon, C k -conjugacy of holomorphic flows near a singularity
  6. Frédéric Bosio, Variétés complexes compactes : une généralisation de la construction de Meersseman et López de Medrano-Verjovsky
  7. Emmanuel Paul, Classification topologique des germes de formes logarithmiques génériques
  8. Laurent Stolovitch, Sur un théorème de Dulac
  9. Jean Martinet, Jean-Pierre Ramis, Classification analytique des équations différentielles non linéaires résonnantes du premier ordre

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