On the topological stability and shadowing in zero-dimensional spaces
classification
🧮 math.DS
keywords
shadowingstabilitytopologicalpropertiesspaceszero-dimensionalcantorcounter-examples
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In this paper, we examine the notion of topological stability and its relation to the shadowing properties in zero-dimensional spaces. Several counter-examples on the topological stability and the shadowing properties are given. Also, we prove that any topologically stable (in a modified sense) homeomorphism of a Cantor space exhibits only simple typical dynamics.
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