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On Stability of Small Periodic Solutions

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Abstract

In this paper, we consider normal time-periodic systems of ordinary differential equations whose right-hand sides smoothly depend on phase variables and small parameters. Branching conditions for small periodic solution of the system are found. Lyapunov stability tests for small solutions with respect to parameters or variables are established. Our reasoning is based on the analysis of the first nonlinear approximation of the monodromy operator.

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Authors and Affiliations

  1. Ryazan State University named for S. A. Esenin, Ryazan, Russia

    V. V. Abramov

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  1. V. V. Abramov
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Correspondence to V. V. Abramov.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 148, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory” (Ryazan, September 15–18, 2016), 2018.

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Abramov, V.V. On Stability of Small Periodic Solutions. J Math Sci 248, 375–381 (2020). https://doi.org/10.1007/s10958-020-04876-0

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  • DOI: https://doi.org/10.1007/s10958-020-04876-0

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