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The topology of holomorphic flows with singularity

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References

  1. A. D. Brjuno, Analytical form of differential equations,Trudy Moscow Math. Obšč (Trans. Moscow Math. Soc.), vol. 25 (1971), p. 131–288.

    Google Scholar 

  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.

  3. Topological properties ofR 2-actions are studied in:C. Camacho, OnR k ×Z l-actions,Proceed. Symp. on Dynamical Systems, Salvador 1971, Ed. Peixoto, p. 23–70.G. Palis, Linearly induced vector fields andR 2-actions on spheres, to appear inJ. Diff. Geom.C. Camacho, Structural stability theorems for integrable differential forms on 3-manifolds, to appear inTopology.

  4. H. Dulac, Solutions d’un système d’équations différentielles dans le voisinage des valeurs singulières,Bull. Soc. Math. France,40 (1912), 324–383.

    Google Scholar 

  5. J. Guckenheimer, Hartman’s theorem for complex flows in the Poincaré domain,Compositio Math.,24 (1972), p. 75–82.

    MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  7. Topological properties ofreal linear flows onR n are studied in:N. H. Kuiper,Manifolds Tokyo, Proceedings Int. Conference, Math. Soc. Japan (1973), p. 195–204, and:N. N. Ladis,Differentialnye Uravnenya Volg. (1973), p. 1222–1235.

  8. D. Lieberman, Holomorphic vector fields on projective varieties,Proc. Symp. Pure Math., XXX (1976), 273–276.

    Google Scholar 

  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.

    Google Scholar 

  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.

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

  15. Ю. С. Ильященко ЭАМЕЧАНИЯ О ТОПОЛоГИИ ОСОЯЫХ ТОЧЕК АНАЛИТИЧЕСКИХ ДИФФЕРЕНЦИАЛьНЫХ УРАВЕНИЙ В КОМПЛЕКСНОЙ ОьЛАСТИ И ТЕОРЕМА ЛАДИСА,Фенкццональныŭ аналц¶rt; ц ео прулоценця, T. 11, ВЫН 2, 1977, 28–38.

    Google Scholar 

  16. J. Guckenheimer, On holomorphic vector fields onCP(2),An. Acad. Brasil. Cienc.,42 (1970), p. 415–420.

    Google Scholar 

  17. F. Dumortier, R. Roussarie, Smooth linearization of germs ofR 2-actions and holomorphic vector fields, to appear.

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Authors and Affiliations

  1. Instituto de Matemática Pura et Aplicada, Rio de Janeiro

    Cesar Camacho & Jacob Palis

  2. Institut des Hautes Études Scientifiques, Bures-sur-Yvette

    Nicolaas H. Kuiper

Authors
  1. Cesar Camacho
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  2. Nicolaas H. Kuiper
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  3. Jacob Palis
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Additional information

This research was partially supported by CNPQ (Brásil) and CNRS (France).

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Camacho, C., Kuiper, N.H. & Palis, J. The topology of holomorphic flows with singularity. Publications Mathématiques de L’Institut des Hautes Scientifiques 48, 5–38 (1978). https://doi.org/10.1007/BF02684312

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  • DOI: https://doi.org/10.1007/BF02684312

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