C1-stably shadowable chain components are hyperbolic

Let f be a diffeomorphism on a closed manifold, and p be a hyperbolic periodic point of f. Denote Cf(p) the chain component of f that contains p. We say Cf(p) is C1-stably shadowable if there is a C1-neighborhood U of f such that for every g∈U, Cg(pg) has the shadowing property, where pg is the continuation of p. We prove in this paper that if Cf(p) is C1-stably shadowable, then Cf(p) is hyperbolic.