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Generalization of the Second Bogolyubov's Theorem for Non-Almost Periodic Systems

David N. Cheban·Jinqiao Duan·Anatoly Gherco
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Abstract

The article is devoted to the generalization of the second Bogolyubov's theorem to non-almost periodic dynamical systems. We prove the analog of the second Bogolyubov's theorem for recurrent or pseudo recurrent dynamical systems in Banach spaces. Namely, we obtain the relation between a recurrent dynamical system and its averaged dynamical system. We also study existence of recurrent and pseudo recurrent motions (including special cases of periodic, quasi-periodic and almost periodic motions) in related nonautonomous systems.

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David N. Cheban, Jinqiao Duan, Anatoly Gherco. 2004-09-13. Generalization of the Second Bogolyubov's Theorem for Non-Almost Periodic Systems. https://arxiv.org/abs/math/0409213

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