Volume-preserving diffeomorphisms with inverse shadowing

Let f be a volume-preserving diffeomorphism of a closed C-infinity n-dimensional Riemannian manifold M. In this paper, we prove the equivalence between the following conditions: (a) f belongs to the C-1-interior of the set of volume-preserving diffeomorphisms which satisfy the inverse shadowing property with respect to the continuous methods, (b) f belongs to the C-1-interior of the set of volume-preserving diffeomorphisms which satisfy the weak inverse shadowing property with respect to the continuous methods, (c) f belongs to the C-1-interior of the set of volume-preserving diffeomorphisms which satisfy the orbital inverse shadowing property with respect to the continuous methods, (d) f is Anosov.