Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SPECTRAL DECOMPOSITION FOR HOMEOMORPHISMS ON NON-METRIZABLE TOTALLY DISCONNECTED SPACES

  • Oh, Jumi (Department of Mathematics Sungkyunkwan University)
  • Received : 2022.03.04
  • Accepted : 2022.04.15
  • Published : 2022.09.01
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Abstract

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.

Keywords

Acknowledgement

The author was supported by the National Research Foundation of Korea grant funded by the MEST 2015R1A3A2031159 and NRF 2019R1A2C1002150.

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