Geodesic
Spaces of $\omega $-limit sets of graph maps
Jie-Hua Mai1 ; Song Shao2
1 Institute of Mathematics Shantou University Shantou, Guangdong, 515063, P.R. China
2 Department of Mathematics University of Science and Technology of China Hefei, Anhui, 230026, P.R. China
Fundamenta Mathematicae, Tome 196 (2007) no. 1, pp. 91-100.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm196-1-2
Keywords: dynamical system general set omega limit sets closed hyperspace closed subsets paper study graph family omega limit sets graph map closed respect hausdorff metric

Jie-Hua Mai 1 ; Song Shao 2

1 Institute of Mathematics Shantou University Shantou, Guangdong, 515063, P.R. China
2 Department of Mathematics University of Science and Technology of China Hefei, Anhui, 230026, P.R. China 
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Jie-Hua Mai; Song Shao. Spaces of $\omega $-limit sets of graph maps. Fundamenta Mathematicae, Tome 196 (2007) no. 1, pp. 91-100. doi : 10.4064/fm196-1-2. http://geodesic.mathdoc.fr/articles/10.4064/fm196-1-2/

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