On the global structure of invariant regions of flows with asymptotically stable attractors (Q1961441)

The authors study some properties of the positively invariant regions of continuous dynamical systems having stable attractors. They show that the global structure of a positively invariant compact set is rather simple in many important cases. Especially, when they contain an asymptotically stable global attractor, they have trivial shape if the ambient space is a Banach space or a contractible manifold.