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Differential Equations

, Volume 53, Issue 13, pp 1703–1714 | Cite as

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

  • A. A. Maltseva
  • V. Reitmann
Control Theory
  • 15 Downloads

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.

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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Faculty of Mathematics and MechanicsSaint Petersburg State UniversityPeterhofRussia

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