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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Ailing Qi, Department of Mathematics, Civil Aviation University of China, Tianjin, China
Xuewei Ju, Department of Mathematics, Civil Aviation University of China, Tianjin, China
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.
Local Approximate Forward Attractors of Nonautonomous Dynamical Systems, American Journal of Applied Mathematics.
Vol. 8, No. 5,
2020, pp. 278-283.
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