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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Volume 254, Pages 111–129 (Mi tm104)  
This article is cited in 12 scientific papers (total in 12 papers)

Dynamics of Local Groups of Conformal Mappings and Generic Properties of Differential Equations on $\mathbb C^2$

A. A. Shcherbakov

Institute of Physical Chemistry and Electro Chemistry, Russian Academy of Sciences
Full-text PDF (574 kB) Citations (12)
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Abstract: This paper is a survey of the present state of the problems related to the generic properties of foliations defined on $\mathbb C^2$ by algebraic differential equations. We prove that the properties of density, absolute rigidity, and existence of a countable set of complex limit cycles are inherent in all equations except possibly for the union of some real algebraic set and real analytic set of codimension at least two in the space of coefficients.
Received in October 2005
English version:
Proceedings of the Steklov Institute of Mathematics, 2006, Volume 254, Pages 103–120
DOI: https://doi.org/10.1134/S0081543806030047
Bibliographic databases:
UDC: 517.927.7
Language: Russian
Citation: A. A. Shcherbakov, “Dynamics of Local Groups of Conformal Mappings and Generic Properties of Differential Equations on $\mathbb C^2$”, Nonlinear analytic differential equations, Collected papers, Trudy Mat. Inst. Steklova, 254, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 111–129; Proc. Steklov Inst. Math., 254 (2006), 103–120
Citation in format AMSBIB
\Bibitem{Shc06}
\by A.~A.~Shcherbakov
\paper Dynamics of Local Groups of Conformal Mappings and Generic Properties of Differential Equations on~$\mathbb C^2$
\inbook Nonlinear analytic differential equations
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2006
\vol 254
\pages 111--129
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm104}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2301001}
\elib{https://elibrary.ru/item.asp?id=13512234}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 254
\pages 103--120
\crossref{https://doi.org/10.1134/S0081543806030047}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33749380871}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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