Diffeomorphisms with the average-shadowing property on two-dimensional closed manifolds (Q5928728)

The goal of this paper is to analyze the dynamics of diffeomorphisms satisfying the average-shadowing property on a two-dimensional closed manifold. Let \({\mathcal {AS}}({\mathcal M})\) be the \(C^1\) interior of the set of all \(f\in \text{Diff}(M)\) having the average-shadowing property, where \({\mathcal M}\) is a two-dimensional closed manifold. The author shows \({\mathcal {AS}}({\mathcal M})\) is characterized as the set of all Anosov diffeomorphisms.