Chain components with stably limit shadowing property are hyperbolic

摘要

Let f be a diffeomorphism on a closed smooth manifold M. In this paper, we show that f has the C 1 -stably limit shadowing property on the chain component C f ( p ) of f containing a hyperbolic periodic point p, if and only if C f ( p ) is a hyperbolic basic set. MSC:37C50, 34D10.