The asymptotic average-shadowing property and transitivity for flows

The asymptotic average-shadowing property is introduced for flows and the relationships between this property and transitivity for flows are investigated. It is shown that a flow on a compact metric space is chain transitive if it has positively (or negatively) asymptotic average-shadowing property and a positively (resp. negatively) Lyapunov stable flow is positively (resp. negatively) topologically transitive provided it has positively (resp. negatively) asymptotic average-shadowing property. Furthermore, two conditions for which a flow is a minimal flow are obtained. (C) 2008 Elsevier Ltd. All rights reserved.