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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 322, Pages 195–205
DOI: https://doi.org/10.4213/tm4345 (Mi tm4345) 		 
A Topological–Analytical Method for Proving Averaging Theorems on an Infinite Time Interval in a Degenerate Case

Ivan Yu. Polekhinabcd

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia
c Lomonosov Moscow State University, Moscow, 119991 Russia
d P. G. Demidov Yaroslavl State University, Sovetskaya ul. 14, Yaroslavl, 150003 Russia
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DOI: https://doi.org/10.4213/tm4345
Abstract: We present a topological–analytical method for proving some results of the N. N. Bogolyubov averaging method for the case of an infinite time interval. The essence of the method is to combine topological methods of proving the existence of a periodic solution applied to the averaged system with Bogolyubov's theorem on the averaging on a finite time interval. The proposed approach allows us to dispense with the nondegeneracy condition for the Jacobi matrix from the classical theorems of the averaging method.
Keywords: averaging, averaging on an infinite interval, degenerate case, asymptotic stability, elliptic fixed point, center.
Funding agency Grant number
Russian Science Foundation 21-71-30011
The work was supported by the Russian Science Foundation under grant no. 21-71-30011, https://rscf.ru/en/project/21-71-30011/, and performed at the P. G. Demidov Yaroslavl State University.
Received: February 13, 2023
Revised: February 13, 2023
Accepted: May 2, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 322, Pages 188–197
DOI: https://doi.org/10.1134/S0081543823040168
Bibliographic databases:
Document Type: Article
UDC: 517.928.7
Language: Russian
Citation: Ivan Yu. Polekhin, “A Topological–Analytical Method for Proving Averaging Theorems on an Infinite Time Interval in a Degenerate Case”, Modern Methods of Mechanics, Collected papers. On the occasion of the 90th birthday of Academician Andrei Gennad'evich Kulikovskii, Trudy Mat. Inst. Steklova, 322, Steklov Math. Inst., Moscow, 2023, 195–205; Proc. Steklov Inst. Math., 322 (2023), 188–197
Citation in format AMSBIB
\Bibitem{Pol23}
\by Ivan~Yu.~Polekhin
\paper A Topological--Analytical Method for Proving Averaging Theorems on an Infinite Time Interval in a Degenerate Case
\inbook Modern Methods of Mechanics
\bookinfo Collected papers. On the occasion of the 90th birthday of Academician Andrei Gennad'evich Kulikovskii
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 322
\pages 195--205
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4345}
\crossref{https://doi.org/10.4213/tm4345}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4677605}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 322
\pages 188--197
\crossref{https://doi.org/10.1134/S0081543823040168}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85180236095}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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