Exploring the asymptotic average shadowing property.

The main aim of this paper is to relate a recently introduced notion of the asymptotic average shadowing property (AASP) with other notions known from topological dynamics. For a compact metric space X and a continuous map [image omitted] we prove the following facts: If f has the AASP and the minimal points of f are dense in X then f is totally transitive.If f is a surjection and has the specification property then f has the AASP.If f is c-expansive and has the shadowing property then f is mixing if and only if f has the AASP. [ABSTRACT FROM AUTHOR]