We study transitive non-minimal ℕ-actions and ℤ-actions. We show that there are such actions whose non-transitive points are periodic and whose topological entropy is positive. It turns out that such actions can be obtained by perturbing minimal systems under some reasonable assumptions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-1-9,
author = {Tomasz Downarowicz and Xiangdong Ye},
title = {When every point is either transitive or periodic},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {137-150},
zbl = {1008.37006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-1-9}
}
Tomasz Downarowicz; Xiangdong Ye. When every point is either transitive or periodic. Colloquium Mathematicae, Tome 91 (2002) pp. 137-150. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-1-9/