Asymptotically stable sets and attractors of inverse limit dynamical systems

Abstract

In this paper we study asymptotically stable sets and attractors of inverse limit dynamical system which is  induced from dynamical system on a compact metric space. We give the implication of asymptotically stable sets and attractors between inverse limit dynamical systems and original systems. More precisely, the inverse limit system has asymptotically stable sets implies original system has asymptotically stable sets. Also, we prove that the inverse limit system has attractors implies original system has attractors.