Symplectic diffeomorphisms with limit shadowing

Abstract

Let f be a symplectic diffeomorphism on a closed C ∞ 2n-dimensional Riemannian manifold M . In this paper, we show that f is Anosov if any of the following statements holds: f belongs to the C 1 -interior of the set of symplectic diffeomorphisms satisfying the limit shadowing property or f belongs to the C 1 -interior of the set of symplectic diffeomorphisms satisfying the limit weak shadowing property or f belongs to the C 1 -interior of the set of symplectic diffeomorphisms satisfying the s-limit shadowing property.