English

On the topological stability and shadowing in zero-dimensional spaces

Dynamical Systems 2018-05-28 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1805.10098,
  title  = {On the topological stability and shadowing in zero-dimensional spaces},
  author = {Noriaki Kawaguchi},
  journal= {arXiv preprint arXiv:1805.10098},
  year   = {2018}
}
R2 v1 2026-06-23T02:08:15.831Z