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Topological stability and shadowing of zero-dimensional dynamical systems

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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.

    Mathematics Subject Classification: 54H20, 37C50.

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