Mathematics of the USSR-Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mathematics of the USSR-Sbornik, 1969, Volume 9, Issue 3, Pages 365–378
DOI: https://doi.org/10.1070/SM1969v009n03ABEH001288
(Mi sm3625)
 

This article is cited in 11 scientific papers (total in 11 papers)

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

Yu. S. Ilyashenko
References:
Abstract: In this work we construct an open set $V$ in the space of coefficients $A_n$ of the equations $\frac{dw}{dz}=\frac{P_n(z,w)}{Q_n(z,w)}$ such that on the solutions of an arbitrary equation $\alpha\in V$ there exist a countable number of homotopically distinct limit cycles. Also, for each natural number $N$ we construct an open set $V_N\subset A_n$ such that an arbitrary equation $\alpha\in V_N$ has a Petrovskii–Landis genus which exceeds $N$.
Bibliography: 9 titles.
Received: 04.02.1969
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1969, Volume 80(122), Number 3(11), Pages 388–404
Bibliographic databases:
Document Type: Article
UDC: 517.92
MSC: 34C07, 34C05
Language: English
Original paper language: Russian
Citation: 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”, Mat. Sb. (N.S.), 80(122):3(11) (1969), 388–404; Math. USSR-Sb., 9:3 (1969), 365–378
Citation in format AMSBIB
\Bibitem{Ily69}
\by Yu.~S.~Ilyashenko
\paper 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
\jour Mat. Sb. (N.S.)
\yr 1969
\vol 80(122)
\issue 3(11)
\pages 388--404
\mathnet{http://mi.mathnet.ru/sm3625}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=259239}
\zmath{https://zbmath.org/?q=an:0202.09201|0214.09404}
\transl
\jour Math. USSR-Sb.
\yr 1969
\vol 9
\issue 3
\pages 365--378
\crossref{https://doi.org/10.1070/SM1969v009n03ABEH001288}
Linking options:
  • https://www.mathnet.ru/eng/sm3625
  • https://doi.org/10.1070/SM1969v009n03ABEH001288
  • https://www.mathnet.ru/eng/sm/v122/i3/p388
  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:661
    Russian version PDF:143
    English version PDF:8
    References:58
    First page:3
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024