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Nelin. Dinam., 2020, Volume 16, Number 1, Pages 181–194 (Mi nd705)  

Mathematical problems of nonlinearity

Intrinsic Shape Property of Global Attractors in Metrizable Spaces

N. Shekutkovski, M. Shoptrajanov

Ss. Cyril and Methodius University, Arhimedova St. 3, Skopje 1000, R.N.Macedonia

Abstract: This paper concerns the connection between shape theory and attractors for semidynamical systems in metric spaces. We show that intrinsic shape theory from [6] is a convenient framework to study the global properties which the attractor inherits from the phase space. Namely, following [6] we’ll improve some of the previous results about the shape of global attractors in arbitrary metrizable spaces by using the intrinsic approach to shape which combines continuity up to a covering and the corresponding homotopies of first order.

Keywords: intrinsic shape, regular covering, continuity over a covering, attractor, proximate net

DOI: https://doi.org/10.20537/nd200114

Full text: PDF file (667 kB)
References: PDF file   HTML file

MSC: 54H20, 54C56, 37B20, 37B25
Received: 12.07.2019
Accepted:02.12.2019

Citation: N. Shekutkovski, M. Shoptrajanov, “Intrinsic Shape Property of Global Attractors in Metrizable Spaces”, Nelin. Dinam., 16:1 (2020), 181–194

Citation in format AMSBIB
\Bibitem{SheSho20}
\by N. Shekutkovski, M. Shoptrajanov
\paper Intrinsic Shape Property of Global Attractors in Metrizable Spaces
\jour Nelin. Dinam.
\yr 2020
\vol 16
\issue 1
\pages 181--194
\mathnet{http://mi.mathnet.ru/nd705}
\crossref{https://doi.org/10.20537/nd200114}
\elib{http://elibrary.ru/item.asp?id=43618869}


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