For a self-map of a compactum we give a necessary and sufficient condition for the chain recurrent set to be precisely the set of periodic points.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-2-2, author = {Katsuya Yokoi}, title = {The chain recurrent set for maps of compacta}, journal = {Annales Polonici Mathematici}, volume = {92}, year = {2007}, pages = {123-131}, zbl = {1129.37023}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-2-2} }
Katsuya Yokoi. The chain recurrent set for maps of compacta. Annales Polonici Mathematici, Tome 92 (2007) pp. 123-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-2-2/