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Mat. Sb. (N.S.), 1984, Volume 123(165), Number 4, Pages 534–548 (Mi msb2035)  

This article is cited in 3 scientific papers (total in 3 papers)

Orbital analytic nonequivalence of saddle resonance vector fields in $(\mathbf C^2,0)$

P. M. Elizarov


Abstract: This article examines germs of holomorphic vector fields fo the form
$$ z\frac\partial{\partial z}+w(-1+zw+z^2w^2P(z,w))\frac\partial{\partial w} $$
under the assumption that the support of the power series $P(z,w)$ lies either above the bisector of the first quadrant of the integer lattice $\mathbf Z_+^2$, or below it. Necessary conditions (imposed on the coefficients of $P(z,w)$) are formulated for orbital analytic equivalence of vector fields of the type indicated; these are obtained with the help of approximate calculation of the Écalle–Voronin functional moduli for the analytic classification of germs of holomorphic mappings which are monodromy transformations of the vector fields considered.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 51:2, 533–547

Bibliographic databases:

UDC: 517.9+517.5
MSC: Primary 58F14; Secondary 34C99
Received: 09.02.1983

Citation: P. M. Elizarov, “Orbital analytic nonequivalence of saddle resonance vector fields in $(\mathbf C^2,0)$”, Mat. Sb. (N.S.), 123(165):4 (1984), 534–548; Math. USSR-Sb., 51:2 (1985), 533–547

Citation in format AMSBIB
\Bibitem{Eli84}
\by P.~M.~Elizarov
\paper Orbital analytic nonequivalence of saddle resonance vector fields in~$(\mathbf C^2,0)$
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 123(165)
\issue 4
\pages 534--548
\mathnet{http://mi.mathnet.ru/msb2035}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=740677}
\zmath{https://zbmath.org/?q=an:0569.34009}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 51
\issue 2
\pages 533--547
\crossref{https://doi.org/10.1070/SM1985v051n02ABEH002873}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. S. Ilyashenko, “Dulac's memoir “On limit cycles” and related problems of the local theory of differential equations”, Russian Math. Surveys, 40:6 (1985), 1–49  mathnet  crossref  mathscinet  adsnasa
    2. S. I. Trifonov, “Divergence of Dulac's rows”, Math. USSR-Sb., 69:1 (1991), 37–56  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. L Billi, E Todesco, G Turchetti, J Phys A Math Gen, 27:18 (1994), 6215  crossref  zmath  adsnasa
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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