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

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

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
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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
2. S. I. Trifonov, “Divergence of Dulac's rows”, Math. USSR-Sb., 69:1 (1991), 37–56
3. L Billi, E Todesco, G Turchetti, J Phys A Math Gen, 27:18 (1994), 6215
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