The asymptotic average-shadowing property is introduced for flows and the relationshipsbetween this property and transitivity for flows are investigated. It is shown that a flow ona compact metric space is chain transitive if it has positively (or negatively) asymptoticaverage-shadowing property and a positively (resp. negatively) Lyapunov stable flow ispositively (resp. negatively) topologically transitive provided it has positively (resp. nega-tively) asymptotic average-shadowing property. Furthermore, two conditions for which aflow is a minimal flow are obtained.
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