Abstract Group Actions

In this paper, we study the properties of the dynamical system under the action of theabstract group. The main results are the following:(1) Under the action of the abstract group,we obtain some sufficient conditions,necessaryand sufficient conditions such that the dynamical system is sensitive.(2) Under the action of the abstract group,we investigate the relationships between themixing property,chaos of (X, d) and the mixing property,chaos of (K, H),...