Various shadowing properties for positively expansive maps

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• 作者：Sakai ; Kazuhiro
• 关键词：37B99 ; 37C50 ; 37D20 ; 54H20 ; 37H99 ; Average shadowing ; Compact metrizable space ; Expanding ; Limit shadowing ; s-limit shadowing ; Lipschitz shadowing ; Positively expansive ; Pseudo-orbit ; Shadowing ; Strong shadowing
• 刊名：Topology and its Applications
• 出版年：2003
• 出版时间：June 1, 2003
• 年：2003
• 卷：131
• 期：1
• 页码：15-31
• 全文大小：160 K

文摘

In this paper, various shadowing properties are considered for a positively expansive map on a compact metrizable space. We show that the Lipschitz shadowing property, the s-limit shadowing property and the strong shadowing property are all equivalent to the (usual) shadowing property for a positively expansive map. Furthermore, for a positively expansive open map, the average shadowing property is shown.