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Mathematics of the USSR-Izvestiya, 1987, Volume 28, Issue 3, Pages 609–623
DOI: https://doi.org/10.1070/IM1987v028n03ABEH000905
(Mi im1522)
 

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

On an almost periodic perturbation on an infinite-dimensional torus

D. A. Tarkhov
References:
Abstract: A well-known result due to V. I. Arnol'd on the reducibility of a weakly perturbed system of differential equations on a finite-dimensional torus is generalized first to the case when the number of equations is infinite, and, second, to the case when the perturbation is an almost periodic function of time. The reduction is effected by Kolmogorov's method of successive substitutions. Conditions are obtained for the convergence of the method for this problem. It is shown that almost all (in a certain sense) bases of frequencies satisfy the requisite condition.
Bibliography: 10 titles
Received: 23.01.1984
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1986, Volume 50, Issue 3, Pages 617–632
Bibliographic databases:
UDC: 517.928+517.937
MSC: Primary 58F30; Secondary 34C50, 34C40, 34C20
Language: English
Original paper language: Russian
Citation: D. A. Tarkhov, “On an almost periodic perturbation on an infinite-dimensional torus”, Izv. Akad. Nauk SSSR Ser. Mat., 50:3 (1986), 617–632; Math. USSR-Izv., 28:3 (1987), 609–623
Citation in format AMSBIB
\Bibitem{Tar86}
\by D.~A.~Tarkhov
\paper On an almost periodic perturbation on an infinite-dimensional torus
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 3
\pages 617--632
\mathnet{http://mi.mathnet.ru/im1522}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=854598}
\zmath{https://zbmath.org/?q=an:0605.58037|0633.58041}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 3
\pages 609--623
\crossref{https://doi.org/10.1070/IM1987v028n03ABEH000905}
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  • https://doi.org/10.1070/IM1987v028n03ABEH000905
  • https://www.mathnet.ru/eng/im/v50/i3/p617
  • 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 Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:288
    Russian version PDF:93
    English version PDF:9
    References:50
    First page:3
     
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