ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Almost Automorphic Dynamics in Almost Periodic Cocycles with One-dimensional Inertial Manifold


Mikhail Mikhailovich Anikushin

Postgraduate student, research engineer at the Department
of Applied Cybernetics, Faculty of Mathematics and Mechanics,
St. Petersburg State University


We study omega-limit and minimal sets of skew-product semiflows associated to cocycles in Banach spaces, which admit one-dimensional inertial manifolds. Our main aim is to extend for such cocycles classical results of W. Shen and Y. Yi on almost automorphy of minimal sets arising in the case of scalar almost periodic ODEs and scalar almost periodic parabolic equations in one-dimensional domains.We give applications for ODEs, delay equations and semilinear parabolic equations. Conditions for the existence of inertial manifolds are given in our adjacent works. In applications, these conditions are verified with the aid of recently obtained versions of the Frequency Theorem.



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