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http://dx.doi.org/10.5666/KMJ.2014.54.2.333

On the Omega Limit Sets for Analytic Flows  

Choy, Jaeyoo (Department of Mathematics, Kyungpook National University)
Chu, Hahng-Yun (Department of Mathematics, Chungnam National University)
Publication Information
Kyungpook Mathematical Journal / v.54, no.2, 2014 , pp. 333-339 More about this Journal
Abstract
In this paper, we describe the characterizations of omega limit sets (= ${\omega}$-limit set) on $\mathbb{R}^2$ in detail. For a local real analytic flow ${\Phi}$ by z' = f(z) on $\mathbb{R}^2$, we prove the ${\omega}$-limit set from the basin of a given attractor is in the boundary of the attractor. Using the result of Jim$\acute{e}$nez-L$\acute{o}$pez and Llibre [9], we can completely understand how both the attractors and the ${\omega}$-limit sets from the basin.
Keywords
attractors; ${\omega}$-limit sets; analytic flows;
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Times Cited By KSCI : 1  (Citation Analysis)
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