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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Ikeda, H. Equivalent Conditions for Ω-Inverse Limit Stability. Journal of Dynamics and Differential Equations 11, 239–254 (1999). https://doi.org/10.1023/A:1021925312468
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DOI: https://doi.org/10.1023/A:1021925312468