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Mat. Zametki, 1968, Volume 4, Issue 6, Pages 741–750 (Mi mz6795)  

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

Density of an individual solution and ergodicity of a family of solutions to the equation $d\eta/d\xi=P(\xi, \eta)/Q(\xi, \eta)$

Yu. S. Ilyashenko

M. V. Lomonosov Moscow State University

Abstract: The paper provides a sharpened proof of M. G. Khudai–Verenov's theorem on the density in $C^2$ of solutions to the equation $d\eta/d\xi=F/Q$ on condition that this equation has two singular points at infinity whose characteristic numbers satisfy certain constraints of the incommensurability type.

Full text: PDF file (761 kB)

English version:
Mathematical Notes, 1968, 4:6, 934–938

Bibliographic databases:

UDC: 517.9
Received: 19.12.1967

Citation: Yu. S. Ilyashenko, “Density of an individual solution and ergodicity of a family of solutions to the equation $d\eta/d\xi=P(\xi, \eta)/Q(\xi, \eta)$”, Mat. Zametki, 4:6 (1968), 741–750; Math. Notes, 4:6 (1968), 934–938

Citation in format AMSBIB
\Bibitem{Ily68}
\by Yu.~S.~Ilyashenko
\paper Density of an~individual solution and ergodicity of a~family of solutions to the equation $d\eta/d\xi=P(\xi,\,\eta)/Q(\xi,\,\eta)$
\jour Mat. Zametki
\yr 1968
\vol 4
\issue 6
\pages 741--750
\mathnet{http://mi.mathnet.ru/mz6795}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=247176}
\zmath{https://zbmath.org/?q=an:0186.41402}
\transl
\jour Math. Notes
\yr 1968
\vol 4
\issue 6
\pages 934--938
\crossref{https://doi.org/10.1007/BF01110832}


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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, “An example of eqations $\frac{dw}{dz}=\frac{P_n(z,w)}{Q_n(z,w)}$ having a countable number of limit cycles and arbitrarily large Petrovskii–Landis genus”, Math. USSR-Sb., 9:3 (1969), 365–378  mathnet  crossref  mathscinet  zmath
    2. T. Golenishcheva-Kutuzova, V. Kleptsyn, “Minimality and ergodicity of a generic analytic foliation of $\mathbb C^2$”, Ergodic Theory and Dynamical Systems, 28:5 (2008), 1533–1544  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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