TY - JOUR

T1 - Existence and Dimension Properties of a Global B-Pullback Attractor for a Cocycle Generated by a Discrete Control System

AU - Maltseva, A. A.

AU - Reitmann, V.

N1 - Funding Information: This work was supported by the Russian Science Foundation grant no. 14-21-00041 and by the German Academic Exchange Service (DAAD). Publisher Copyright: © 2017, Pleiades Publishing, Ltd. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - We consider cocycles on finite-dimensional manifolds generated by discrete-time control systems. Frequency conditions for the existence of a global B-pullback attractor for such cocycles considered over a general base system on a metric space are given. Upper bounds for the Hausdorff dimension of the global B-pullback attractor of a discrete cocycle are obtained using the transfer function of the linear part of the cocycle and the discrete Kalman–Yakubovich–Popov frequency theorem.

AB - We consider cocycles on finite-dimensional manifolds generated by discrete-time control systems. Frequency conditions for the existence of a global B-pullback attractor for such cocycles considered over a general base system on a metric space are given. Upper bounds for the Hausdorff dimension of the global B-pullback attractor of a discrete cocycle are obtained using the transfer function of the linear part of the cocycle and the discrete Kalman–Yakubovich–Popov frequency theorem.

UR - http://www.scopus.com/inward/record.url?scp=85044169234&partnerID=8YFLogxK

U2 - 10.1134/S001226611713002X

DO - 10.1134/S001226611713002X

M3 - Article

AN - SCOPUS:85044169234

VL - 53

SP - 1703

EP - 1714

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 13

ER -