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February  2005, 13(2): 533-540. doi: 10.3934/dcds.2005.13.533

Various shadowing properties and their equivalence

Keonhee Lee 1, and  Kazuhiro Sakai 2,

1. 

Department of Mathematics, Chungnam National University, Daejeon, 305-764, South Korea
2. 

Department of Mathematics, Utsunomiya University, Utsunomiya 321-8505

Received  June 2004 Revised  February 2005 Published  April 2005

In this paper, various shadowing properties are considered for expansive homeomorphisms. More precisely, we show that the continuous shadowing property, the Lipschitz shadowing property, the limit shadowing property and the strong shadowing property are all equivalent to the (usual) shadowing property for expansive homeomorphisms on compact metric spaces.
Keywords: strong shadowing, limit shadowing, Pseudo-orbit, Lipschitz shadowing, continuous shadowing, expansive., shadowing.
Mathematics Subject Classification: Primary: 37B99, 37C15, 37C50, 37D20; Secondary: 54H2.
Citation: Keonhee Lee, Kazuhiro Sakai. Various shadowing properties and their equivalence. Discrete & Continuous Dynamical Systems - A, 2005, 13 (2) : 533-540. doi: 10.3934/dcds.2005.13.533
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