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Izv. Akad. Nauk SSSR Ser. Mat., 1990, Volume 54, Issue 2, Pages 378–395 (Mi izv1099)  

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

On integral manifolds of multifrequency oscillatory systems

A. M. Samoilenko, R. I. Petrishin


Abstract: Conditions are found for the existence of an integral manifold for a nonlinear oscillatory system with slowly varying frequencies, and an algorithm for constructing it is described. A theorem is proved on the conditional asymptotic stability of the integral manifold with respect to a set of initial values for the slow variables. Smoothness is also studied, and bounds on the partial derivatives of the function that describes the integral manifold are obtained.

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English version:
Mathematics of the USSR-Izvestiya, 1991, 36:2, 391–409

Bibliographic databases:

UDC: 517.9
MSC: Primary 34C45; Secondary 58F27
Received: 25.05.1988

Citation: A. M. Samoilenko, R. I. Petrishin, “On integral manifolds of multifrequency oscillatory systems”, Izv. Akad. Nauk SSSR Ser. Mat., 54:2 (1990), 378–395; Math. USSR-Izv., 36:2 (1991), 391–409

Citation in format AMSBIB
\Bibitem{SamPet90}
\by A.~M.~Samoilenko, R.~I.~Petrishin
\paper On integral manifolds of multifrequency oscillatory systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1990
\vol 54
\issue 2
\pages 378--395
\mathnet{http://mi.mathnet.ru/izv1099}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1062519}
\zmath{https://zbmath.org/?q=an:0721.34027|0708.34027}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..36..391S}
\transl
\jour Math. USSR-Izv.
\yr 1991
\vol 36
\issue 2
\pages 391--409
\crossref{https://doi.org/10.1070/IM1991v036n02ABEH002027}


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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. A. M. Samoilenko, “N. N. Bogolyubov and non-linear mechanics”, Russian Math. Surveys, 49:5 (1994), 109–154  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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