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Russian Academy of Sciences. Izvestiya Mathematics, 1994, Volume 43, Issue 3, Pages 455–470
DOI: https://doi.org/10.1070/IM1994v043n03ABEH001575
(Mi im826)
 

This article is cited in 1 scientific paper (total in 1 paper)

On quasiperiodic solutions of the matrix Riccati equation

V. S. Pronkin
References:
Abstract: The matrix Riccati equation
\begin{equation} \dot X+Xf(t)X+(A_0+A(t))X+\lambda l(t)=0 \tag{1} \end{equation}
is considered, where $X$ is an unknown vector, $A_0$ is a constant diagonal matrix whose elements are pairwise distinct imaginary numbers, the coefficients $f(t)$, $A(t)$, and $l(t)$ are matrices whose elements are Arnold'd functions, and $\lambda$ is a small complex parameter. Newton's method is used to prove that (1) has quasiperiodic solutions with the exception of finitely many rays. By using the quasiperiodic solutions obtained it is proved that, with the exception of finitely many rays, the system of differential equations $\dot X=(P_0+\lambda P(t))X$ is reducible, where $P(t)$ is a matrix whose elements are Arnol'd functions, and $\lambda$ is a small complex parameter.
Received: 17.04.1992
Bibliographic databases:
UDC: 517.925.52+517.923
MSC: 34A34, 34C20, 34C28
Language: English
Original paper language: Russian
Citation: V. S. Pronkin, “On quasiperiodic solutions of the matrix Riccati equation”, Russian Acad. Sci. Izv. Math., 43:3 (1994), 455–470
Citation in format AMSBIB
\Bibitem{Pro93}
\by V.~S.~Pronkin
\paper On quasiperiodic solutions of the matrix Riccati equation
\jour Russian Acad. Sci. Izv. Math.
\yr 1994
\vol 43
\issue 3
\pages 455--470
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\crossref{https://doi.org/10.1070/IM1994v043n03ABEH001575}
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\zmath{https://zbmath.org/?q=an:0820.34025}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1994IzMat..43..455P}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994QK21500004}
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  • https://doi.org/10.1070/IM1994v043n03ABEH001575
  • https://www.mathnet.ru/eng/im/v57/i6/p64
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:436
    Russian version PDF:98
    English version PDF:10
    References:64
    First page:4
     
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