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

2004/09/13 by David N. Cheban, Cheban, David N., Jinqiao Duan +3
Mathematics · #34D40 #34D45 #35B40 #58F10 #58F12 #58F39 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AP #math.DS #msc:34D40 #msc:34D45 #msc:35B35 #msc:35B40 #msc:58F10 #msc:58F12 #msc:58F39 #primary:34D20 #secondary: 35B35

paper · pdf · doi:10.48550/arxiv.math/0409213

May 16, 2002

arxiv created 2004/09/13 · arxiv updated 2009/12/01

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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