Abstract
In this paper, we consider systems of linear differential equations with periodic coefficients depending on a small parameter. We propose new approaches to the problem of constructing a monodromy matrix that lead to new effective formulas for calculating multipliers of the system studies. We present a number of applications in problems of the perturbation theory of linear operators, in the analysis of stability of linear differential equations with periodic coefficients, in the problem of constructing the stability domains of linear dynamical systems, etc.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 163, Differential Equations, 2019.
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Yumagulov, M.G., Ibragimova, L.S. & Belova, A.S. Methods for Studying the Stability of Linear Periodic Systems Depending on a Small Parameter. J Math Sci 258, 115–127 (2021). https://doi.org/10.1007/s10958-021-05540-x
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DOI: https://doi.org/10.1007/s10958-021-05540-x
Keywords and phrases
- differential equation
- periodic system
- Hamiltonian system
- monodromy matrix
- multiplier
- stability
- small parameter