The topology of holomorphic flows with singularity
Camacho, Cesar ; Kuiper, Nicolaas H. ; Palis, Jacob
Publications Mathématiques de l'IHÉS, Tome 48 (1978), p. 5-38 / Harvested from Numdam
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@article{PMIHES_1978__48__5_0,
     author = {Camacho, Cesar and Kuiper, Nicolaas Hendrik and Palis, Jacob},
     title = {The topology of holomorphic flows with singularity},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {48},
     year = {1978},
     pages = {5-38},
     mrnumber = {80j:58045},
     zbl = {0411.58018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_1978__48__5_0}
}

Camacho, Cesar; Kuiper, Nicolaas H.; Palis, Jacob. The topology of holomorphic flows with singularity. Publications Mathématiques de l'IHÉS, Tome 48 (1978) pp. 5-38. http://gdmltest.u-ga.fr/item/PMIHES_1978__48__5_0/

[1] A. D. Brjuno, Analytical form of differential equations, Trudy Moscow Math. Obšč (Trans. Moscow Math. Soc.), vol. 25 (1971), p. 131-288. | MR 51 #13365 | Zbl 0272.34018

[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. | MR 54 #1301 | Zbl 0353.32015

[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] H. Dulac, Solutions d'un système d'équations différentielles dans le voisinage des valeurs singulières, Bull. Soc. Math. France, 40 (1912), 324-383. | JFM 43.0391.01 | Numdam

[5] J. Guckenheimer, Hartman's theorem for complex flows in the Poincaré domain, Composito Math., 24 (1972), p. 75-82. | Numdam | MR 46 #920 | Zbl 0239.58007

[6] A real analogue of theorem III is the classical Grobman-Hartman theorem : P. Hartman, Proc. AMS, 11 (1960), p. 610-620. | MR 22 #12279

[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] D. Lieberman, Holomorphic vector fields on projective varieties, Proc. Symp. Pure Math., XXX (1976), 273-276. | MR 56 #12337 | Zbl 0365.32021

[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] J. Palis, S. Smale, Structural stability theorems, Global Analysis, Symp. Pure Math., AMS, vol. XIV (1970), p. 223-231. | MR 42 #2505 | Zbl 0214.50702

[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] 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] C. L. Siegel, Über die Normalform analytischer Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Göttingen, Nachr. Akad. Wiss., Math. Phys. Kl. (1952), p. 21-30. | MR 15,222b | Zbl 0047.32901

[14] C. L. Siegel, J. Moser, Celestial mechanics (1971) (English edition of : C. L. SIEGEL, Vorlesungen über Himmelsmechanik, 1954, Springer Verlag).

[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] J. Guckenheimer, On holomorphic vector fields on CP(2), An. Acad. Brasil. Cienc., 42 (1970), p. 415-420. | MR 44 #2254 | Zbl 0205.54101

[17] F. Dumortier, R. Roussarie, Smooth linearization of germs of R2-actions and holomorphic vector fields, to appear. | Numdam | Zbl 0418.58015