Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 148, Pages 3–9 (Mi into296)  
This article is cited in 2 scientific papers (total in 2 papers)

On Stability of Small Periodic Solutions

V. V. Abramov

Ryazan State University named for S. A. Esenin
Full-text PDF (161 kB) Citations (2)
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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. Conditions of branching of small periodic solution of the system are found. Stability tests for small Lyapunov 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.
Keywords: system of ordinary differential equations, small parameter, monodromy operator, branching of a periodic solution, stability.
English version:
Journal of Mathematical Sciences, 2020, Volume 248, Issue 4, Pages 375–381
DOI: https://doi.org/10.1007/s10958-020-04876-0
Bibliographic databases:
Document Type: Article
UDC: 517.925.51
MSC: 34C23, 34C25, 34D99
Language: Russian
Citation: V. V. Abramov, “On Stability of Small Periodic Solutions”, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 148, VINITI, M., 2018, 3–9; Journal of Mathematical Sciences, 248:4 (2020), 375–381
Citation in format AMSBIB
\Bibitem{Abr18}
\by V.~V.~Abramov
\paper On Stability of Small Periodic Solutions
\inbook Proceedings of the International Conference ``Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,'' Ryazan, September 15--18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 148
\pages 3--9
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into296}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3847701}
\transl
\jour Journal of Mathematical Sciences
\yr 2020
\vol 248
\issue 4
\pages 375--381
\crossref{https://doi.org/10.1007/s10958-020-04876-0}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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