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Reducibility of Linear Differential Systems to Linear Differential Equations

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Abstract

Lyapunov reducibility of any bounded and sometimes unbounded linear homogeneous differential system to some bounded linear homogeneous differential equation is established. The preservation of the additional property of periodicity of coefficients is guaranteed, and for two-dimensional or complex systems the constancy of their coefficients is preserved. The differences in feasibility of asymptotic and generalized Lyapunov reducibility from Lyapunov one are indicated.

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Acknowledgments

The author is grateful to V. V. Bykov for valuable remarks contributed to significant improvement in the text of the paper.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    I. N. Sergeev

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  1. I. N. Sergeev
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Correspondence to I. N. Sergeev.

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Russian Text © The Author(s). 2019. published in Vestnik Moskovskogo Universiteta. Matematika. Mekhanika. 2019. Vol. 74, No. 3, pp. 39–44.

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Sergeev, I.N. Reducibility of Linear Differential Systems to Linear Differential Equations. Moscow Univ. Math. Bull. 74, 121–126 (2019). https://doi.org/10.3103/S0027132219030045

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  • DOI: https://doi.org/10.3103/S0027132219030045

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