Geodesic
First steps towards the averaging with respect to a part of the coordinates
Theoretical and applied mechanics, Tome 52 (2025) no. 1, p. 115

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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.
DOI : 10.2298/TAM250110005P
Classification : 34C29
Keywords: periodic systems, averaging, rapid oscillations, infinite time interval, topological methods in dynamics 
Ivan Polekhin. First steps towards the averaging with respect to a part of the coordinates. Theoretical and applied mechanics, Tome 52 (2025) no. 1, p. 115 . doi: 10.2298/TAM250110005P
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