Topological stability of semigroup actions and shadowing
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910914872082432 |
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| author | Ceccherini-Silberstein, Tullio Coornaert, Michel Phung, Xuan Kien |
| author_facet | Ceccherini-Silberstein, Tullio Coornaert, Michel Phung, Xuan Kien |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_07984 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological stability of semigroup actions and shadowing Ceccherini-Silberstein, Tullio Coornaert, Michel Phung, Xuan Kien Dynamical Systems Group Theory 20M30, 54H15, 37B05, 37D20, 37B10, 37B65, 37C20, 37B51 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. |
| title | Topological stability of semigroup actions and shadowing |
| topic | Dynamical Systems Group Theory 20M30, 54H15, 37B05, 37D20, 37B10, 37B65, 37C20, 37B51 |
| url | https://arxiv.org/abs/2502.07984 |