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Mathematics of the USSR-Sbornik, 1976, Volume 28, Issue 2, Pages 140–152
DOI: https://doi.org/10.1070/SM1976v028n02ABEH001644
(Mi sm2744)
 

This article is cited in 8 scientific papers (total in 8 papers)

Analytic unsolvability of the stability problem and the problem of topological classification of the singular points of analytic systems of differential equations

Yu. S. Il'yashenko
References:
Abstract: In this paper the analytic unsolvability of the Ljapunov stability problem and the problem of topological classification of the singular points is proved for the analytic system of differential equations
\begin{equation} \dot x=v(x),\qquad x\in R^n. \end{equation}

This means that there does not exist an analytic criterion that, from a finite segment $v_N(x)$ of the Taylor series of the field $v(x)$ at the origin, would permit one to say whether the singular point $0$ of equation (1) is stable or unstable, or that the stability investigation must consider a longer segment of the Taylor series. In other words, there does not exist an analytic criterion permitting one to distinguish stable, unstable and neutral jets of analytic vector fields with singular point $0$.
Bibliography: 4 titles.
Received: 09.10.1974
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1976, Volume 99(141), Number 2, Pages 162–175
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 34C05, 34D20, 34D30
Language: English
Original paper language: Russian
Citation: Yu. S. Il'yashenko, “Analytic unsolvability of the stability problem and the problem of topological classification of the singular points of analytic systems of differential equations”, Mat. Sb. (N.S.), 99(141):2 (1976), 162–175; Math. USSR-Sb., 28:2 (1976), 140–152
Citation in format AMSBIB
\Bibitem{Ily76}
\by Yu.~S.~Il'yashenko
\paper Analytic unsolvability of the stability problem and the problem of topological classification of the singular points of analytic systems of differential equations
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 99(141)
\issue 2
\pages 162--175
\mathnet{http://mi.mathnet.ru/sm2744}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=405509}
\zmath{https://zbmath.org/?q=an:0332.34042}
\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 28
\issue 2
\pages 140--152
\crossref{https://doi.org/10.1070/SM1976v028n02ABEH001644}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1976EM69100002}
Linking options:
  • https://www.mathnet.ru/eng/sm2744
  • https://doi.org/10.1070/SM1976v028n02ABEH001644
  • https://www.mathnet.ru/eng/sm/v141/i2/p162
  • This publication is cited in the following 8 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:424
    Russian version PDF:135
    English version PDF:9
    References:60
    First page:3
     
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