Topological stability of semigroup actions and shadowing
Dynamical Systems
2025-04-22 v2 Group Theory
Abstract
We investigate expansiveness, topological stability, and shadowing for continuous actions of semigroups on compact Hausdorff spaces. We characterize semigroups for which all full shifts are expansive. We show that every expansive continuous monoid action on a compact Hausdorff space which has the shadowing property is topologically stable, and that a subshift with finite alphabet over a monoid has the shadowing property if and only if it is of finite type.
Keywords
Cite
@article{arxiv.2502.07984,
title = {Topological stability of semigroup actions and shadowing},
author = {Tullio Ceccherini-Silberstein and Michel Coornaert and Xuan Kien Phung},
journal= {arXiv preprint arXiv:2502.07984},
year = {2025}
}