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On the Omega Limit Sets for Analytic Flows

  • Choy, Jaeyoo ;
  • Chu, Hahng-Yun
  • Received : 2014.02.13
  • Accepted : 2014.05.22
  • Published : 2014.06.23

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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Cited by

  1. A TOPOLOGICAL CHARACTERIZATION OF ­Ω-LIMIT SETS ON DYNAMICAL SYSTEMS vol.27, pp.3, 2014, https://doi.org/10.14403/jcms.2014.27.3.523

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)