Limit Shadowing Property For Uniformly Hyperbolic System

Let / be a diffeomorphism on a Riemannian manifold. In this paper, we study the limit shadowing property of /. It is shown that (1). / has the limit shadowing property with respect to some 8 > 0 on a neighborhood of the hyperbolic set;(2). if / is C1-structurally stable, then / has the limit shadowing property with respect to some δ > o.