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J. Korean Math. Soc. 2022; 59(5): 987-996

Online first article June 3, 2022      Printed September 1, 2022

https://doi.org/10.4134/JKMS.j220105

Copyright © The Korean Mathematical Society.

Spectral decomposition for homeomorphisms on non-metrizable totally disconnected spaces

Jumi Oh

Sungkyunkwan University

Abstract

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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: Expansive, shadowing, Smale's spectral decomposition theorem

MSC numbers: Primary 37D05, 37D20

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

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