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Uniform persistence and repellors for maps. (English) Zbl 0678.58024

Summary: 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.

MSC:

37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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