• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.85-90
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• 2022

In this article, we consider the notion of expansiveness on compact metric spaces for symbolically point of view. And we show that a homeomorphism is symbolically countably expansive if and only if it is symbolically measure expansive. Moreover, we prove that a homeomorphism is symbolically N-expansive if and only if it is symbolically measure N-expanding.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.987-996
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• 2022

We introduce the notions of symbolic expansivity and symbolic shadowing for homeomorphisms on non-metrizable compact spaces which are generalizations of expansivity and shadowing, respectively, for metric spaces. The main result is to generalize the Smale's spectral decomposition theorem to symbolically expansive homeomorphisms with symbolic shadowing on non-metrizable compact Hausdorff totally disconnected spaces.