First steps towards the averaging with respect to a part of the coordinates

The problem of averaging on an infinite time interval is considered. The classical results on averaging proved by N.N. Bogoluybov are generalized to the case in which only a part of the coordinates in the phase space remains close to the equilibrium position of the averaged system. We call...

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Main Author: Polekhin Ivan
Format: Article
Language:English
Published: Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade 2025-01-01
Series:Theoretical and Applied Mechanics
Subjects:
Online Access:https://doiserbia.nb.rs/img/doi/1450-5584/2025/1450-55842500005P.pdf
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author Polekhin Ivan
author_facet Polekhin Ivan
author_sort Polekhin Ivan
collection DOAJ
description The problem of averaging on an infinite time interval is considered. The classical results on averaging proved by N.N. Bogoluybov are generalized to the case in which only a part of the coordinates in the phase space remains close to the equilibrium position of the averaged system. We call this the averaging with respect to a part of the coordinates. The results are based on some topological ideas combined with the standard theorem on averaging on a finite time interval.
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institution Kabale University
issn 1450-5584
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language English
publishDate 2025-01-01
publisher Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade
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spelling doaj-art-d9b1dbf2ed234a7a9ef6b38c7b963ee52025-08-20T03:58:54ZengSerbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, BelgradeTheoretical and Applied Mechanics1450-55842406-09252025-01-0152111512510.2298/TAM250110005P1450-55842500005PFirst steps towards the averaging with respect to a part of the coordinatesPolekhin Ivan0https://orcid.org/0009-0008-4979-8144Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia + Moscow Institute of Physics and Technology, Dolgoprudny, Russia + Lomonosov Moscow State University, Moscow, Russia + P.G. Demidov Yaroslavl State University, Yaroslavl, RussiaThe problem of averaging on an infinite time interval is considered. The classical results on averaging proved by N.N. Bogoluybov are generalized to the case in which only a part of the coordinates in the phase space remains close to the equilibrium position of the averaged system. We call this the averaging with respect to a part of the coordinates. The results are based on some topological ideas combined with the standard theorem on averaging on a finite time interval.https://doiserbia.nb.rs/img/doi/1450-5584/2025/1450-55842500005P.pdfperiodic systemsaveragingrapid oscillationsinfinite time intervaltopological methods in dynamics.
spellingShingle Polekhin Ivan
First steps towards the averaging with respect to a part of the coordinates
Theoretical and Applied Mechanics
periodic systems
averaging
rapid oscillations
infinite time interval
topological methods in dynamics.
title First steps towards the averaging with respect to a part of the coordinates
title_full First steps towards the averaging with respect to a part of the coordinates
title_fullStr First steps towards the averaging with respect to a part of the coordinates
title_full_unstemmed First steps towards the averaging with respect to a part of the coordinates
title_short First steps towards the averaging with respect to a part of the coordinates
title_sort first steps towards the averaging with respect to a part of the coordinates
topic periodic systems
averaging
rapid oscillations
infinite time interval
topological methods in dynamics.
url https://doiserbia.nb.rs/img/doi/1450-5584/2025/1450-55842500005P.pdf
work_keys_str_mv AT polekhinivan firststepstowardstheaveragingwithrespecttoapartofthecoordinates