TOPOLOGICAL COMPLEXITY OF SEMIGROUP ACTIONS
Xinhua Yan, Lianfa He · Journal of the Korean Mathematical Society · 2008
In this paper, we study the complexity of semigroup actions using complexity functions of open covers. The main results are as follows: (1) A dynamical system is equicontinuous if and only if any open cover has bounded complexity; (2) Weak-mixing implies scattering; (3) We get a criterion for the scattering property.