Let (X,f) be a dynamical system. In general the set of all ω-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 ω-limit sets of a graph map is closed with respect to the Hausdorff metric.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm196-1-2,
author = {Jie-Hua Mai and Song Shao},
title = {Spaces of $\omega$-limit sets of graph maps},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {91-100},
zbl = {1128.37027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm196-1-2}
}
Jie-Hua Mai; Song Shao. Spaces of ω-limit sets of graph maps. Fundamenta Mathematicae, Tome 193 (2007) pp. 91-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm196-1-2/