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

Existence and Dimension Properties of a Global B-Pullback Attractor for a Cocycle Generated by a... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

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

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Publisher
Pleiades Publishing
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
D.O.I.
10.1134/S001226611713002X
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Differential EquationsSpringer Journals

Published: Mar 14, 2018

References

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