Uniform Persistence and Repellors for Maps
Josef Hofbauer, Joseph W.-H. So · Proceedings of the American Mathematical Society · 1989
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.