Local Approximate Forward Attractors of Nonautonomous Dynamical Systems
American Journal of Applied Mathematics
Volume 8, Issue 5, October 2020, Pages: 278-283
Received: May 6, 2020; Accepted: Jul. 24, 2020; Published: Sep. 25, 2020
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Authors
Ailing Qi, Department of Mathematics, Civil Aviation University of China, Tianjin, China
Xuewei Ju, Department of Mathematics, Civil Aviation University of China, Tianjin, China
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Abstract
Pullback dynamics of nonautonomous dynamical systems has been considerably developed. However, it is still a tough job to study forward dynamics of nonautonomous dynamical systems, since forward attractors were only obtained in some particular cases. In the paper, under some reasonable conditions, it is shown that closing to a local pullback attractor, there is an approximate forward attractor. Specifically, let ϕ be a cocycle semiflow on a Banach space X with driving system θ on a base space P. Suppose that the base space P is compact and ϕ is uniformly asymptotically compact. Let A(∙) be a local pullback attractor with being compact. We prove that every ε-extended neighborhood Aε(∙) of A(∙) will forward attract every bounded set B(∙) that is pullback attracted by A(∙). We then call Aε(∙) an approximate forward attractor of ϕ.
Keywords
Nonautonomous Dynamical Systems, Pullback Attractors, Approximate Forward Attractors
To cite this article
Ailing Qi, Xuewei Ju, Local Approximate Forward Attractors of Nonautonomous Dynamical Systems, American Journal of Applied Mathematics. Vol. 8, No. 5, 2020, pp. 278-283. doi: 10.11648/j.ajam.20200805.16
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Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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