Weak inverse shadowing and genericity

Taeyoung Choi; Sungsook Kim; Keonhee Lee

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Bull. Korean Math. Soc. 2006; 43(1): 43-52

Printed March 1, 2006

Weak inverse shadowing and genericity

Taeyoung Choi, Sungsook Kim, and Keonhee Lee

Chungnam National University, Paichai University, Chungnam National University

Abstract

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Abstract

We study the genericity of the first weak inverse shadowing property and the second weak inverse shadowing property in the space of homeomorphisms on a compact metric space, and show that every shift homeomorphism does not have the first weak inverse shadowing property but it has the second weak inverse shadowing property.

Keywords: shadowing, inverse shadowing, weak inverse shadowing, generic

MSC numbers: Primary 37C20; Secondary 37C50