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Mathematics of the USSR-Sbornik, 1990, Volume 65, Issue 2, Pages 369–384
DOI: https://doi.org/10.1070/SM1990v065n02ABEH001147 (Mi sm1792) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Lyapunov exponents as functions of a parameter

V. M. Millionshchikov
English version PDF (941 kB) Citations (18)
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DOI: https://doi.org/10.1070/SM1990v065n02ABEH001147
Abstract: The author proves the typical nature, in the sense of Baire category, of the upper semicontinuity of the Lyapunov exponents of a family of endomorphisms of a metrized vector bundle, considered as a function of a parameter on which a point of the base of this bundle continuously depends. It is proved that the Lyapunov exponents, as functions of this parameter, belong to the second Baire class. An application of these abstract theorems to the Lyapunov exponents of nonlinear systems of differential equations continuously depending on a parameter is given.
Bibliography: 14 titles.
Received: 29.03.1988
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1988, Volume 137(179), Number 3(11), Pages 364–380
Bibliographic databases:
Document Type: Article
UDC: 517.938
MSC: Primary 34D05, 34D20, 26A21; Secondary 34C11, 34C35, 54C50
Language: English
Original paper language: Russian
Citation: V. M. Millionshchikov, “Lyapunov exponents as functions of a parameter”, Mat. Sb. (N.S.), 137(179):3(11) (1988), 364–380; Math. USSR-Sb., 65:2 (1990), 369–384
Citation in format AMSBIB
\Bibitem{Mil88}
\by V.~M.~Millionshchikov
\paper Lyapunov exponents as functions of a parameter
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 137(179)
\issue 3(11)
\pages 364--380
\mathnet{http://mi.mathnet.ru/sm1792}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=976517}
\zmath{https://zbmath.org/?q=an:0705.34058}
\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 65
\issue 2
\pages 369--384
\crossref{https://doi.org/10.1070/SM1990v065n02ABEH001147}
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  • https://doi.org/10.1070/SM1990v065n02ABEH001147
  • https://www.mathnet.ru/eng/sm/v179/i3/p364
    • This publication is cited in the following 18 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:1100
    Russian version PDF:594
    English version PDF:13
    References:57
    First page:3
     
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