When every point is either transitive or periodic
Volume 93 / 2002
Colloquium Mathematicum 93 (2002), 137-150
MSC: Primary 37B05, 54H20.
DOI: 10.4064/cm93-1-9
Abstract
We study transitive non-minimal ${\mathbb N}$-actions and ${\mathbb Z}$-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.
