Proceedings of the American Mathematical Society 107 , No. 4. (Dec. 1989), pp. 1137-1142.
Abstract. We establish conditions for an isolated invariant set M of a map to be a repellor. The conditions are first formulated in terms of the stable set of M. They are then refined in two ways by considering (i) a Morse decomposition for M, and (ii) the invariantly connected components of the chain recurrent set of M. These results generalize and unify earlier persistence results.