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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 3, Pages 617–632 (Mi izv1522)  

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


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

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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:3, 609–623

Bibliographic databases:

UDC: 517.928+517.937
MSC: Primary 58F30; Secondary 34C50, 34C40, 34C20
Received: 23.01.1984

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/izv1522}
\mathscinet{http://www.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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    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. D. A. Tarkhov, “Reducibility of a linear system of differential equations with odd almost periodic coefficients”, Math. Notes, 60:1 (1996), 81–88  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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