Some Dynamical Properties Of The Minimal Continuous Semi-flows

In this paper, we study the topological dynamical properties of the minimal continuous semi flow on a compact metric space. Firstly, we connect the minimal continuous semi-flow with the minimal sets of its time-one map. Secondly, by using the connection, we prove that the minimal continuous semi-flow is the minimal continuous flow if its time-one map is open, and for any minimal continuous semi-flow, there is an invariant residual set such that the restriction to the set is a minimal continuous flow. Finally, we show that any noninvertiblely, minimal continuous semi-flow is the factor of a minimal continuous flow, and there is no noninvertiblely, minimal continuous semi-flow on the two-dimensional compact manifold.