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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2013, Volume 13, Issue 2, Pages 28–44 (Mi vngu140)  

This article is cited in 2 scientific papers (total in 2 papers)

Singular Points and First Integrals of Holomorphic Dynamical Systems

E. P. Volokitinab, V. M. Cheresizab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: We study the complex system $\dot z=F(z)$ near the singular point which is a multiple zero or a pole of the function $F(z)$ on the phase plane. We consider trajectories of such systems at infinity. We construct first integrals of polynomial systems using the method of Darboux. We use our results to sketch phase portraits.

Keywords: nonhyperbolic singular points, separatrices, elliptic sectors, hyperbolic sectors, first integrals.

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English version:
Journal of Mathematical Sciences, 2014, 203:4, 605–620

Document Type: Article
UDC: 517.925
Received: 07.05.2012

Citation: E. P. Volokitin, V. M. Cheresiz, “Singular Points and First Integrals of Holomorphic Dynamical Systems”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 13:2 (2013), 28–44; J. Math. Sci., 203:4 (2014), 605–620

Citation in format AMSBIB
\Bibitem{VolChe13}
\by E.~P.~Volokitin, V.~M.~Cheresiz
\paper Singular Points and First Integrals of Holomorphic Dynamical Systems
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2013
\vol 13
\issue 2
\pages 28--44
\mathnet{http://mi.mathnet.ru/vngu140}
\transl
\jour J. Math. Sci.
\yr 2014
\vol 203
\issue 4
\pages 605--620
\crossref{https://doi.org/10.1007/s10958-014-2162-y}


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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. E. P. Volokitin, “Neogranichennye resheniya polinomialnykh sistem Koshi–Rimana”, Sib. elektron. matem. izv., 11 (2014), 494–507  mathnet
    2. E. P. Volokitin, S. A. Treskov, V. M. Cheresiz, “Kvadratichnye i kubicheskie sistemy, udovletvoryayuschie usloviyam Koshi–Rimana”, Sib. elektron. matem. izv., 12 (2015), 45–63  mathnet  crossref
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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