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This article is cited in 3 scientific papers (total in 3 papers)
Baire classes of Lyapunov invariants
V. V. Bykov Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
It is shown that no relations exist (apart from inherent ones) between Baire classes of Lyapunov transformation invariants in the compact-open and uniform topologies on the space of linear differential systems.
It is established that if a functional on the space of linear differential systems with the compact-open topology is the repeated limit of a multisequence of continuous functionals, then these can be chosen to be determined by the values of system coefficients on a finite interval of the half-line (one for each functional).
It is proved that the Lyapunov exponents cannot be represented as the limit of a sequence of (not necessarily continuous) functionals such that each of these depends only on the restriction of the system to a finite interval of the half-line.
Bibliography: 28 titles.
Keywords:
linear differential systems, asymptotic equivalence, Lyapunov exponents, Baire classes.
Received: 01.09.2016 and 06.12.2016
Citation:
V. V. Bykov, “Baire classes of Lyapunov invariants”, Mat. Sb., 208:5 (2017), 38–62; Sb. Math., 208:5 (2017), 620–643
Linking options:
https://www.mathnet.ru/eng/sm8809https://doi.org/10.1070/SM8809 https://www.mathnet.ru/eng/sm/v208/i5/p38
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Abstract page: | 441 | Russian version PDF: | 57 | English version PDF: | 22 | References: | 70 | First page: | 14 |
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