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
DOI:10.20537/nd200114