Geodesic
Baire classes of Lyapunov invariants
Sbornik. Mathematics, Tome 208 (2017) no. 5, pp. 620-643

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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
Mots-clés : Baire classes. 
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     author = {V. V. Bykov},
     title = {Baire classes of {Lyapunov} invariants},
     journal = {Sbornik. Mathematics},
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     volume = {208},
     number = {5},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_5_a1/}
}
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V. V. Bykov. Baire classes of Lyapunov invariants. Sbornik. Mathematics, Tome 208 (2017) no. 5, pp. 620-643. http://geodesic.mathdoc.fr/item/SM_2017_208_5_a1/