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Mathematics of the USSR-Sbornik, 1975, Volume 27, Issue 3, Pages 325–338
DOI: https://doi.org/10.1070/SM1975v027n03ABEH002517
(Mi sm3715)
 

This article is cited in 7 scientific papers (total in 7 papers)

On the density of solutions of an equation in CP2

B. Müller
References:
Abstract: In this paper we consider the system
˙u=P(u),
where u=(u0,u1,u2)C3, P=(P0,P1,P2) and the Pi are homogeneous polynomials of degree 2n (n1) with complex coefficients. Let An be the space of coefficients of the right-hand sides of the system (1). Any point αAn defines a system of the form (1).
Our aim in this paper is to show that the property of the solutions of the system (1) being dense in CP2 is locally characteristic, i.e. we prove that in An there exists an open set U such that the solutions of the system (1) with right-hand side αU are everywhere dense in CP2.
This result can be extended without difficulty to the case in which the degree of the homogeneous polynomials appearing in the right-hand side of the system (1) is odd.
Bibliography: 4 titles.
Received: 18.06.1974
Bibliographic databases:
UDC: 517.92
MSC: Primary 34C05; Secondary 34A20
Language: English
Original paper language: Russian
Citation: B. Müller, “On the density of solutions of an equation in CP2”, Math. USSR-Sb., 27:3 (1975), 325–338
Citation in format AMSBIB
\Bibitem{Mul75}
\by B.~M\"uller
\paper On~the density of solutions of an equation in~$\mathbf{CP}^2$
\jour Math. USSR-Sb.
\yr 1975
\vol 27
\issue 3
\pages 325--338
\mathnet{http://mi.mathnet.ru/eng/sm3715}
\crossref{https://doi.org/10.1070/SM1975v027n03ABEH002517}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=466689}
\zmath{https://zbmath.org/?q=an:0319.34006}
Linking options:
  • https://www.mathnet.ru/eng/sm3715
  • https://doi.org/10.1070/SM1975v027n03ABEH002517
  • https://www.mathnet.ru/eng/sm/v140/i3/p363
  • This publication is cited in the following 7 articles:
    1. Aurélien Alvarez, Bertrand Deroin, “Stabilité structurelle du feuilletage de Jouanolou de degré 2”, Publ.math.IHES, 2025  crossref
    2. Nataliya Goncharuk, Yury Kudryashov, “Genera of non-algebraic leaves of polynomial foliations of C2”, Mosc. Math. J., 18:1 (2018), 63–83  mathnet  crossref
    3. N Goncharuk, Yu Kudryashov, “Cheap complex limit cycles”, Nonlinearity, 31:3 (2018), 909  crossref
    4. John Erik Fornæss, Nessim Sibony, “Unique Ergodicity of Harmonic Currents On Singular Foliations of P2”, Geom. Funct. Anal., 19:5 (2010), 1334  crossref
    5. J.E.rik Fornæss, Nessim Sibony, “Riemann Surface Laminations with Singularities”, J Geom Anal, 18:2 (2008), 400  crossref  mathscinet
    6. A. A. Shcherbakov, “Dynamics of Local Groups of Conformal Mappings and Generic Properties of Differential Equations on C2”, Proc. Steklov Inst. Math., 254 (2006), 103–120  mathnet  crossref  mathscinet  zmath  elib
    7. Ilyashenko Y., “Centennial History of Hilbert's 16th Problem”, Bull. Amer. Math. Soc., 39:3 (2002), 301–354  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Russian version PDF:75
    English version PDF:4
    References:50
     
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