Intrinsic Shape Property of Global Attractors in Metrizable Spaces

    Received 30 October 2019; accepted 02 December 2019

    2020, Vol. 16, no. 1, pp.  181-194

    Author(s): Shekutkovski N., Shoptrajanov M.

    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
    Citation: Shekutkovski N., Shoptrajanov M., Intrinsic Shape Property of Global Attractors in Metrizable Spaces, Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 1, pp.  181-194

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