A+ CATEGORY SCIENTIFIC UNIT

Spaces of $\omega $-limit sets of graph maps

Volume 196 / 2007

Jie-Hua Mai, Song Shao Fundamenta Mathematicae 196 (2007), 91-100 MSC: Primary 37E25; Secondary 54B20. DOI: 10.4064/fm196-1-2

Abstract

Let $(X,f)$ be a dynamical system. In general the set of all $\omega $-limit sets of $f$ is not closed in the hyperspace of closed subsets of $X$. In this paper we study the case when $X$ is a graph, and show that the family of $\omega $-limit sets of a graph map is closed with respect to the Hausdorff metric.

Authors

  • Jie-Hua MaiInstitute of Mathematics
    Shantou University
    Shantou, Guangdong, 515063, P.R. China
    e-mail
  • Song ShaoDepartment of Mathematics
    University of Science and Technology of China
    Hefei, Anhui, 230026, P.R. China
    e-mail

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