Journal of Inequalities and Applications
Volume 6 (2001), Issue 5, Pages 507-517

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

Copyright © 2001 Keon-Hee Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.