On the structure of uniform attractors
This paper presents several results concerning shape properties and properties related to robustness of the uniform attractors of continuous dynamical systems. It is proved that, in certain circumstances, small perturbations of a flow \(\pi\) produce new uniform attractors whose global properties (in the sense of shape theory) are comparable to those of the uniform attractors of \(\pi\). It is also proved that if \(K\) is a minimal compactum then the shape of the closure of every positive semitrajectory in the region of attraction of \(K\) is determined by \(K\). This result does not hold if one considers homotopy type instead of shape. Finally, a classical theorem of Karol Borsuk is used to determine the structure of the set of connected components of uniform attractors.
scientific article; zbMATH DE number 785128