Abstract
Recently we obtained sufficient conditions for an endomorphism to be Ω-inverse limit stable. That is, if an endomorphism f satisfies weak Axiom A and the no-cycles condition, then f is Ω-inverse limit stable. In this paper we give alternative conditions for Ω-inverse limit stability. The following are equivalent: (a) f satisfies weak Axiom A and the no-cycles condition; (b) the chain recurrent set \(CR(f)\) is prehyperbolic; and (c) the closure of the set of ω-limit points of f, L+(f), is prehyperbolic with no cycles.
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