Sensitive dependence on initial of chaotic semi-group actions

Abstract

In this paper, let X a non—empty compact metric place and S a semi-group. By topological transitivity and sensitive dependence on the initial, we introduces a concept of Devaney's chaos. We prove that topologically strong mixing implies Devaney's chaos when semi-group S continuously acts on the compact metric space X. At the same time, we popularize the concept of sensitive dependence on initial.