The average-shadowing property and topological ergodicity for flows (Q2483629)

A theorem on the relationship among the average-shadowing property, the Lyapunov stability and the topological ergodicity is presented. It is known that, in general, the shadowing property is regarded as a kind of stability. The authors show that a system with double stabilities can yet imply a quite strong transitive property, that is, topological ergodicity. As a consequence, such a flow is not sensitive dependent of initial conditions.