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.
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}
}