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Mat. Sb. (N.S.), 1988, Volume 137(179), Number 3(11), Pages 364–380 (Mi msb1792)  

This article is cited in 10 scientific papers (total in 10 papers)

Lyapunov exponents as functions of a parameter

V. M. Millionshchikov


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.

Full text: PDF file (1031 kB)
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English version:
Mathematics of the USSR-Sbornik, 1990, 65:2, 369–384

Bibliographic databases:

UDC: 517.938
MSC: Primary 34D05, 34D20, 26A21; Secondary 34C11, 34C35, 54C50
Received: 29.03.1988

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/msb1792}
\mathscinet{http://www.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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    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. Morozov O., “Baire Class of Lyapunov Exponents on Nonhomogeneous Linear-Systems”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1991, no. 6, 22–30  mathscinet  isi
    2. Millionshchikov V. Sergeev I. Akhmetov M. Artamonov I. Feklin V. Zernov A. Laptinskii V. Sushko V. Ivanov A. Izobov N. Gonchenko S. Shilnikov L. Rozet I. Sadovskii A. Nazarov V. Popova S. Tonkov E. Gonchenko S. Turaev D. Shilnikov L., “Seminar on the Qualitative Theory of Differential-Equations at Moscow-University”, Differ. Equ., 28:11 (1992), 1655–1672  isi
    3. I. A. Galiullin, “Baire class of Lyapunov exponents of mechanical systems containing parameters”, Russian Math. (Iz. VUZ), 45:10 (2001), 10–16  mathnet  mathscinet  zmath  elib
    4. Galiullin I.A., “Uravneniya v variatsiyakh dlya regulyarnykh pretsessii i strukturnaya ustoichivost etikh dvizhenii”, Trudy MAI, 2011, no. 49, 3–3  elib
    5. I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Yu. Goritskii, N. A. Izobov, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, V. V. Palin, N. Kh. Rozov, M. S. Romanov, I. N. Sergeev, E. V. Radkevich, O. S. Rozanova, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Scientific heritage of Vladimir Mikhailovich Millionshchikov”, J. Math. Sci. (N. Y.), 210:2 (2015), 115–134  mathnet  crossref
    6. V. V. Bykov, “Bohl exponents and baire classes of functions”, J. Math. Sci. (N. Y.), 210:2 (2015), 168–185  mathnet  crossref
    7. A. I. Shutova, “A stabilization indices problem”, J. Math. Sci. (N. Y.), 210:3 (2015), 333–339  mathnet  crossref
    8. V. V. Bykov, “Baire classes of Lyapunov invariants”, Sb. Math., 208:5 (2017), 620–643  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. E. A. Barabanov, V. V. Bykov, “Opisanie lineinogo effekta Perrona pri parametricheskikh vozmuscheniyakh, eksponentsialno ubyvayuschikh k nulyu na beskonechnosti”, Tr. IMM UrO RAN, 25, no. 4, 2019, 31–43  mathnet  crossref  elib
    10. V. V. Bykov, “To Millionshchikov's problem on the baire class of central exponents of diffeomorphisms”, Moscow University Mathematics Bulletin, 74:5 (2019), 189–194  mathnet  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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