Abstract
Abstract. In this article, we deal with the notion of ›-limit setsin dynamical systems. We show that the ›-limit set of a compactsubset of a phase space is quasi-attracting. 1. IntroductionThe theory for the notion of attractors is important for the classi-cal theory of dynamical systems. Conley [7] introduced a topologicaldeflnition of attractors for a °ow on a compact metric space. Hurley[9, 10] obtained results which is related to the correspondence betweenattractors and Lyapunov functions on noncompact spaces. Akin [1] andMcGehee [12] obtained many properties of attractors in set-valued dy-namics.The concept of omega-limit set, arising from their ubiquitous applica-tions in dynamical systems, is also an extremely used tool in the abstracttheory of dynamical systems. Especially, the notion of omega-limit setsis much related to the notion of attractors. These notions are used todescribe eventually the positive time behavior for dynamical systems.In recent years, Choy and Chu [4] described the characterizations ofomega-limit sets for analytic °ows on R
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