%0 Journal Article
%T Generalization of the Second Bogolyubov's Theorem for Non-Almost Periodic Systems
%A David N. Cheban
%A Jinqiao Duan
%A Anatoly Gherco
%J Mathematics
%D 2004
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0409213v1