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The topology of holomorphic flows with singularity
Publications Mathématiques de l'IHÉS, Volume 48 (1978), pp. 5-38
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DOI: 10.1007/BF02684312 
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     author = {Cesar Camacho and Nicolaas H. Kuiper and Jacob Palis},
     title = {The topology of holomorphic flows with singularity},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {5--38},
     year = {1978},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {48},
     doi = {10.1007/BF02684312},
     mrnumber = {80j:58045},
     zbl = {0411.58018},
     language = {en},
     url = {https://pmihes.centre-mersenne.org/articles/10.1007/BF02684312/}
}
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Cesar Camacho; Nicolaas H. Kuiper; Jacob Palis. The topology of holomorphic flows with singularity. Publications Mathématiques de l'IHÉS, Volume 48 (1978), pp. 5-38. doi: 10.1007/BF02684312

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

[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. | Zbl | MR

[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 | Numdam

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

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

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

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

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