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

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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Bibliographic Details
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:
periodic systems
averaging
rapid oscillations
infinite time interval
topological methods in dynamics.
Online Access:https://doiserbia.nb.rs/img/doi/1450-5584/2025/1450-55842500005P.pdf
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Summary: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.
ISSN:1450-5584
2406-0925

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