Equivalent Conditions for Ω-Inverse Limit Stability

    loading  Checking for direct PDF access through Ovid

Abstract

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

Related Topics

    loading  Loading Related Articles