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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 5, Pages 1005–1031 (Mi izv1215)  

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

Behavior of conditional stability under a change of the parameters

V. M. Millionshchikov


Abstract: The author proves that the lower semicontinuity with respect to the parameter of certain functions arising in the consideration of families of differential equations is typical (in the Baire category sense). In the case considered these functions are level sets of Lyapunov exponents of points of the space of a metric vector bundle with respect to a given family of endomorphisms. In this case a level set of a function is defined as the set of values of the arguments such that the function is less than a given number. The problem considered in the paper covers many concrete situations.
Bibliography: 16 titles.

Full text: PDF file (3600 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:2, 331–354

Bibliographic databases:

UDC: 517.938
MSC: Primary 34D05, 34D20, 26A21; Secondary 34C11, 34C35, 54C50
Received: 11.03.1988

Citation: V. M. Millionshchikov, “Behavior of conditional stability under a change of the parameters”, Izv. Akad. Nauk SSSR Ser. Mat., 52:5 (1988), 1005–1031; Math. USSR-Izv., 33:2 (1989), 331–354

Citation in format AMSBIB
\Bibitem{Mil88}
\by V.~M.~Millionshchikov
\paper Behavior of conditional stability under a~change of the parameters
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 5
\pages 1005--1031
\mathnet{http://mi.mathnet.ru/izv1215}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=972093}
\zmath{https://zbmath.org/?q=an:0677.34050|0664.34059}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 2
\pages 331--354
\crossref{https://doi.org/10.1070/IM1989v033n02ABEH000833}


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    This publication is cited in the following articles:
    1. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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