A note on the average shadowing property for expansive maps (Q649787)

This paper proves that, given a compact metric space \(X\) and a continuous map \(f:X\rightarrow X\) with the shadowing property, the following five conditions are equivalent: (1) topological transitivity, (2) weak topological mixing, (3) topological mixing, (4) surjectivity and the specification property, (5) surjectivity and the average shadowing property. The paper includes a thorough discussion on how its results complete and extend existing knowledge. Various corollaries are also presented.