Various shadowing properties and their equivalence

Keonhee Lee; Kazuhiro Sakai

doi:10.3934/dcds.2005.13.533

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2005, Volume 13, Issue 2: 533-540. Doi: 10.3934/dcds.2005.13.533

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Various shadowing properties and their equivalence

Keonhee Lee^1, and
Kazuhiro Sakai^2,

1.
Department of Mathematics, Chungnam National University, Daejeon, 305-764
2.
Department of Mathematics, Utsunomiya University, Utsunomiya 321-8505

Received: May 31, 2004

Revised: January 31, 2005

Published: January 2005

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Abstract

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.

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Mathematics Subject Classification: Primary: 37B99, 37C15, 37C50, 37D20; Secondary: 54H20.

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