In this paper, for a continuous semi-flow (heta) on a compact metric space (E) with the asymptotic average-shadowing property (AASP), we show that if the almost periodic points of (heta) are dense in (E) then (heta) is multi-sensitive and syndetically sensitive. Also, we show that if (heta) is a Lyapunov stable semi-flow with the AASP, then the space (E) is trivial. Consequently, a Lyapunov stable semi-flow with the AASP is minimal. Furthermore, we prove that for a syndetically transitive continuous semi-flow on a compact metric space, sensitivity is equivalent to syndetical sensitivity. As an application, we show that for a continuous semi-flow (heta) on a compact metric space (E) with the AASP, if the almost periodic points of (arphi) are dense in (E) then (heta) is syndetically sensitive. {Moreover, we prove that for any continuous semi-flow (heta) on a compact metric space, it has the AASP if and only if so does its inverse limit ((widetilde{E}, widetilde{heta})), and if only if so does its lifting continuous semi-flow ((widehat{E}, widehat{heta})). Also, an example which contains two numerical experiments is given. Our results extend some corresponding and existing ones.
展开▼
