2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72459The 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.May 16, 2002Dynamical SystemsAnalysis of PDEsprimary:34D20, 34D40, 34D45, 58F10, 58F12, 58F39;secondary: 35B35, 35B40text