Some consequences of shadowing and entropy-expansiveness
Dynamical Systems
2025-05-21 v2
Abstract
We show that if a continuous self-map of a compact metric space is h-expansive and satisfies the shadowing property, then every non-empty uniformly rigid subset is zero-dimensional, and hence the set of periodic points is also zero-dimensional if it is not empty.
Keywords
Cite
@article{arxiv.2504.06641,
title = {Some consequences of shadowing and entropy-expansiveness},
author = {Noriaki Kawaguchi},
journal= {arXiv preprint arXiv:2504.06641},
year = {2025}
}
Comments
9 pages, title changed, main result improved, Appendix A added