Shape properties of the boundary of attractors

Abstract

A compact stable attractor K of a continuous flow on a locally compact metric space is shape equivalent to a compact positively invariant neighbourhood P in its basin of attraction, the shape equivalence being induced by the inclusion map. In the present article a simple counterexample is given to show that ∂K is in general not shape equivalent to ∂P , and an inquiry is set afoot as to the circumstances under which ∂K is shape equivalent to or shape dominates ∂P .