Journal of the
Korean Mathematical Society JKMS

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; Shadowin; Smale's spectral decomposition theorem.

MSC numbers: 37D05, 37D20