Some dynamical properties of the minimal continuous semi-flows (Q2572644)

Topological properties of minimal continuous semi-flows on a compact metric space are studied. Main results of the paper: 1) A connection of a minimal continuous semi-flow with minimal sets of the time-one map is established. 2) By using this connection it is proven that the minimal continuous semi-flow is a 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. 3) It is shown that any noninvertible minimal continuous semi-flow is a factor of a minimal continuous flow, and there is no noninvertible minimal continuous semi-flow on a two-dimensional compact manifold.