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.

MSC: 54H20, 54C56, 37B20, 37B25

Received: 12.07.2019
Accepted: 02.12.2019

Language: English

DOI: 10.20537/nd200114

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