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Oscillation, Rotation, and Wandering of Solutions to Linear Differential Systems

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Abstract

For solutions of a linear system on the semi-axis, we introduce a series of Lyapunov exponents that describe the oscillation, rotation, and wandering properties of these solutions. In the case of systems with constant matrices, these exponents are closely related to the imaginary parts of the eigenvalues. We examine the problem on the existence of a similar relationship in the case of piecewise constant of arbitrary systems.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, 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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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 132, Proceedings of International Symposium “Differential Equations–2016,” Perm, 2016.

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Sergeev, I.N. Oscillation, Rotation, and Wandering of Solutions to Linear Differential Systems. J Math Sci 230, 770–774 (2018). https://doi.org/10.1007/s10958-018-3787-z

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  • DOI: https://doi.org/10.1007/s10958-018-3787-z

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