Literature cited
W. Ambrose and S. Kakitani, “Structure and continuity of measurable flows,” Duke Math. J.,1, No. 9, 25–42 (1942).
H. Bohr, Almost-Periodic Functions [in Russian], GTTI, Moscow-Leningrad (1937).
B. F. Bylov, “On the stability of characteristic exponents of systems of linear differential equations,” Doctoral Dissertation, Moscow State Univ. (1954).
B. F. Bylov, R. E. Vinograd, D. M. Grobman, and V. V. Nemytskii, The Theory of Lyapunov Exponents [in Russian], Moscow State Univ. (1954).
B. F. Bylov, “Generalized regular systems,” Diff. Uravn.,7, No. 4, 575–591 (1971).
B. F. Bylov, R. E. Vinograd, V. Ya. Lin, and O. V. Lokutsievskii, “On topological obstructions to block diagonalization of some exponentially split almost-periodic systems,” Preprint No. 69 IPM AN SSSR, Moscow (1977).
Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in a Banach Space [in Russian], Nauka, Moscow (1970).
N. P. Erugin, Linear Systems of Ordinary Differential Equations with Periodic and Quasiperiodic Coefficients [in Russian], Izd. Akad. Nauk BSSR, Minsk (1963).
N. A. Izobov, “Linear systems of ordinary differential equations,” in: Mathematical Analysis [in Russian], Vol. 12, Izd. VINITI, Moscow (1974).
A. N. Kolmogorov and S. V. Fomin, Elements of Function Theory of Functions and Functional Analysis, Graylock (1961).
B. M. Levitan, Almost-Periodic Functions [in Russian], GTTI, Moscow (1953).
J. C. Lillo, “Approximate similarity and almost periodic matrices,” Proc. Am. Math. Soc.,12, No. 3, 400–407 (1961).
A. M. Lyapunov, Collected Works [in Russian], Vol. 2, Izd. Akad. Nauk SSSR, Moscow-Leningrad (1956).
V. M. Millionshchikov, “Statistical regular systems,” Mat. Sb.,75 (117), No. 1, 140–151 (1968).
V. M. Millionshchikov, “The metric theory of linear systems of ordinary differential equations,” Mat. Sb.,77 (119), No. 2, 163–173 (1968).
V. M. Millionshchikov, “A criterion of stability of the probable spectrum of linear systems of differential equations with recurrent coefficients and a criterion of almost reducibility of systems with almost-periodic coefficients,” Mat. Sb.,78 (120), No. 2, 179–201 (1969).
V. M. Millionshchikov, “Proof of the existence of irregular systems of linear differential equations with quasiperiodic coefficients,” Diff. Uravn.,5, No. 11, 1979–1983 (1969).
V. M. Millionshchikov, “Linear systems of ordinary differential equations,” in: International Congress of Mathematicians in Nice, 1970, Nauka, Moscow (1972).
V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], Gostekhizdat, Moscow (1949).
V. L. Novikov, “On almost-reducible systems with almost-periodic coefficients,” Mat. Zametki,16, No. 5, 789–799 (1974).
V. L. Novikov, “A criterion for stability of central exponents of a system of linear differential equations with almost-periodic coefficients,” in: Tr. Seminara im I. G. Petrovskogo, No. 4, Moscow State Univ. (1976), pp. 151–188.
V. I. Oseledets, “A multiplicative ergodic theorem. Characteristic Lyapunov exponents of dynamical systems,” in: Trudy MMO, Vol. 19, Moscow State Univ. (1968), pp. 179–210.
V. A. Rohlin, “Selected questions of the metric theory of dynamical systems,” Ups. Mat.4, No. 2, 57–128 (1949).
N. S. Fal'ko, “On almost-reducible systems with quasiperiodic coefficients,” Diff. Uravn.,14, No. 3, 467–473 (1978).
B. A. Shcherbakov, Topological Dynamics and Poisson Stability of Solutions of Differential Equations [in Russian], Shtinitsa, Kishinev (1972).
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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 7, pp. 199–227, 1981.
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Fal'ko, N.S. Two-dimensional almost-reducible systems with almost-periodic coefficients. J Math Sci 31, 3213–3234 (1985). https://doi.org/10.1007/BF02105142
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DOI: https://doi.org/10.1007/BF02105142