C(l)-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 C(f)(p) the chain component of f that contains p. We say C(f)(p) is C(l)-stably shadowable if there is a C(l)-neighborhood u of f such that for every g is an element of u, C(g)(p(g)) has the shadowing property, where p(g) is the continuation of p. We prove in this paper that if C(f)(p) is C(l)-stably shadowable, then C(f)(p) is hyperbolic. (c) 2008 Elsevier Inc. All rights reserved.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000261314600016&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701MathematicsSCI(E)21ARTICLE1340-35724