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Mat. Sb. (N.S.), 1972, Volume 88(130), Number 4(8), Pages 558–577 (Mi msb3198)  

This article is cited in 12 scientific papers (total in 12 papers)

Fiberings into analytic curves

Yu. S. Ilyashenko

Abstract: 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.

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English version:
Mathematics of the USSR-Sbornik, 1972, 17:4, 551–569

Bibliographic databases:

UDC: 513.6
MSC: Primary 34C05, 32E10; Secondary 34C40, 32E30
Received: 24.06.1971

Citation: Yu. S. Ilyashenko, “Fiberings into analytic curves”, Mat. Sb. (N.S.), 88(130):4(8) (1972), 558–577; Math. USSR-Sb., 17:4 (1972), 551–569

Citation in format AMSBIB
\by Yu.~S.~Ilyashenko
\paper Fiberings into analytic curves
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 88(130)
\issue 4(8)
\pages 558--577
\jour Math. USSR-Sb.
\yr 1972
\vol 17
\issue 4
\pages 551--569

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    This publication is cited in the following articles:
    1. Yu. S. Ilyashenko, “Remarks on the topology of singular points of analytic differential equations in the complex domain and Ladis' theorem”, Funct. Anal. Appl., 11:2 (1977), 105–113  mathnet  crossref  mathscinet  zmath
    2. A. A. Glutsyuk, “The Hyperbolicity of Phase Curves of a Generic Polynomial Vector Field in $\mathbb{C}^n$”, Funct. Anal. Appl., 28:2 (1994), 77–84  mathnet  crossref  mathscinet  zmath  isi
    3. T. S. Firsova, “Topology of Analytic Foliations in $\mathbb C^2$. The Kupka–Smale Property”, Proc. Steklov Inst. Math., 254 (2006), 152–168  mathnet  crossref  mathscinet  elib
    4. Yu. S. Ilyashenko, “Persistence Theorems and Simultaneous Uniformization”, Proc. Steklov Inst. Math., 254 (2006), 184–200  mathnet  crossref  mathscinet  elib
    5. T. Golenishcheva-Kutuzova, V. Kleptsyn, “Minimality and ergodicity of a generic analytic foliation of $\mathbb C^2$”, Ergodic Theory and Dynamical Systems, 28:5 (2008), 1533–1544  crossref  mathscinet  zmath  isi  elib
    6. Marco Brunella, “Nonuniformisable foliations on compact complex surfaces”, Mosc. Math. J., 9:4 (2009), 729–748  mathnet  crossref  mathscinet  zmath
    7. Sergey Ivashkovich, “Vanishing Cycles in Holomorphic Foliations by Curves and Foliated Shells”, Geom. Funct. Anal, 2011  crossref  mathscinet
    8. A. A. Shcherbakov, “Metrics and smooth uniformisation of leaves of holomorphic foliations”, Mosc. Math. J., 11:1 (2011), 157–178  mathnet  crossref  mathscinet
    9. E. M. Chirka, “Holomorphic motions and uniformization of holomorphic families of Riemann surfaces”, Russian Math. Surveys, 67:6 (2012), 1091–1165  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. L. Ortiz-Bobadilla, E. Rosales-González, S. M. Voronin, “Thom's problem for degenerated singular points of holomorphic foliations in the plane”, Mosc. Math. J., 12:4 (2012), 825–862  mathnet  crossref  mathscinet
    11. A. A. Shcherbakov, “Almost complex structures on universal coverings of foliations”, Trans. Moscow Math. Soc., 76:2 (2015), 137–179  mathnet  crossref  elib
    12. A. A. Scherbakov, “Uniformizatsiya sloenii s giperbolicheskimi listami i uravnenie Beltrami s parametrami”, Funkts. analiz i ego pril., 53:3 (2019), 98–100  mathnet  crossref  mathscinet  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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