Journal of Inequalities and Applications 
Volume 6 (2001), Issue 5, Pages 507-517
doi:10.1155/S1025583401000315

Hyperbolic sets with the strong limit shadowing property

Keon-Hee Lee1,2

 1Department of Mathematics, Chungnam National University, Taejon 305-764, Korea
2Department of Mathematics, University of Queensland, Brisbane 4072, QLD , Australia
Received 18 June 1999; Revised 20 January 2000

Abstract

Let ϕ be a C1 dynamical system on a compact smooth manifold M. In this paper we introduce the notions of weak limit shadowing property and strong limit shadowing property of subsets of M which are not equivalent with that of shadowing property, and show that for any hyperbolic submanifold Λ of M the restriction ϕ|Λ is Anosov if and only if Λ has the strong limit shadowing property. Moreover we find hyperbolic sets which have the strong limit shadowing property.