Weakly almost periodic mappings on one- and two-manifolds
Weyl almost periodic points in topological dynamics
When every point is either transitive or periodic
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.