Symplectic diffeomorphisms with inverse shadowing (Q394661)

This article is devoted to the proof of the following theorem: Let \(M\) be a closed \(C^\infty\) \(2n\)-dimensional manifold with Riemannian structure. Let \(f\) be a symplectic diffeomorphism of \(M\). Then the following conditions are equivalent: (1) \(f\) is Anosov, (2) \(f\) lies in the \(C^1\)-interior of the set of symplectic diffeomorphisms with the inverse shadowing property with respect to continuous methods, (3) \(f\) lies in the \(C^1\)-interior of the set of symplectic diffeomorphisms with the orbital inverse shadowing property with respect to continuous methods.