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

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

Determining Modes and Almost Periodic Integrals for Cocycles

Author(s):

Ilya Valeryevich Ermakov

35, fl. 79, Razvodnaya st,
Peterhof, Saint-Petersburg,
198516, Russia
Saint-Petersburg State University
postgraduate student

ilya403@mail.ru

Yuri Nikolaevich Kalinin

70 corp.3, Botanicheskaya st,
Peterhof, Saint-Petersburg,
198516, Russia
Saint-Petersburg State University
postgraduate student

shouganai@mail.ru

Volker Reitmann

70 corp.3, Botanicheskaya st,
Peterhof, Saint-Petersburg,
198516, Russia
Saint-Petersburg State University
professor of the Department of Applied Cybernetics
Prof. Dr.

vreitmann@aol.com

Abstract:

General cocycles on an arbitrary metric space are considered. The notion of determining modes for cocycles on a Hilbert space is introduced and a theorem on the existence of a finite number of determining modes for cocycles is proved. The existence proof of a B-pullback attractor for the microwave heating problem is stated. The notion of an almost periodic integral for a cocycle is introduced and the existence of such an integral for a class of cocycles is proved.

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