Uniform persistence and repellors for maps

Source abstract

We establish conditions for an isolated invariant set M M of a map to be a repellor. The conditions are first formulated in terms of the stable set of M M . They are then refined in two ways by considering (i) a Morse decomposition for M M , and (ii) the invariantly connected components of the chain recurrent set of M M . These results generalize and unify earlier persistence results.