Some results on the average inverse shadowing property and strong ergodicity

Abstract EN

Let (1) and (2) be compact metric spaces, :(1) →(1) and : (2) →(2) be continuous maps.

If and G have dense minimal points and the average inverse shadowing property, we have proved ×G has an average inverse shadowing property, topological transitive and dense minimal points.

Moreover, we have proved is totally strongly ergodic and weakly mixing.