Geodesic
Fiberings into analytic curves
Sbornik. Mathematics, Tome 17 (1972) no. 4, pp. 551-569 
Yu. S. Ilyashenko. Fiberings into analytic curves. Sbornik. Mathematics, Tome 17 (1972) no. 4, pp. 551-569. http://geodesic.mathdoc.fr/item/SM_1972_17_4_a6/
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     author = {Yu. S. Ilyashenko},
     title = {Fiberings into analytic curves},
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     volume = {17},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_17_4_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we study fiberings of analytic manifolds (mainly, Stein manifolds) into analytic curves. The leading special case is a fibering into solutions of the differential equation $\dot z=F(z)$, $z\in\mathbf C^n$, with the right side entire analytic. We introduce two geometrical objects connected with a fibering: the manifold $\widehat\Phi$ of coverings of fibers and the domain of preservation of cycles $\Omega$. The main theorem asserts that under some general assumptions the manifold $\widehat\Phi$ is a Stein manifold. Under the same assumptions the domain $\Omega$ is a Stein space. Figures: 4. Bibliography: 7 titles.

[1] R. Ganning, X. Rossi, Analiticheskie funktsii mnogikh kompleksnykh peremennykh, Mir, Moskva, 1969 | MR

[2] Yu. S. Ilyashenko, “Razrushenie tsiklov v sloeniyakh na analiticheskie krivye”, Matem. sb., 87(129) (1972), 58–66

[3] I. G. Petrovskii, E. M. Landis, “O chisle predelnykh tsiklov uravneniya $dy/dx=P(x,y)/Q(x,u)$, gde $P$ i $Q$ – mnogochleny vtoroi stepeni”, Matem. sb., 37(79) (1955), 209–250 | MR | Zbl

[4] I. G. Petrovskii, E. M. Landis, “Popravki k statyam "O chisle predelnykh tsiklov uravneniya $dy/dx=P(x,y)/Q(x,y)$, gde $P$ i $Q$ – mnogochleny vtoroi stepeni" i "O chisle predelnykh tsiklov uravneniya $dy/dx=P(x,y)/Q(x,u)$, gde $P$ i $Q$ – polinomy"”, Matem. sb., 48(90) (1959), 253–255 | MR | Zbl

[5] H. Rossi, “On envelops of holomorphy”, Comm. Pure Appl. Math., 16 (1963), 9–19 | DOI | MR

[6] G. Stolzenberg, “Uniform approximation on smooth curves”, Acta. Math., 115:3–4 (1966), 185–198 | DOI | MR | Zbl

[7] B. V. Shabat, Vvedenie v kompleksnyi analiz, Nauka, Moskva, 1969 | MR | Zbl