On the subsystems of certain sofic shifts
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918140303114240 |
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| author | Krieger, Wolfgang |
| author_facet | Krieger, Wolfgang |
| contents | For an aperiodic subshift of finite type $Y$ and for a subshift $X$ with topological entropy less than the topological entropy of $Y$, a theorem is proved in Krieger: On the subsystems of topological Markov chains, Ergodic Theory \& dynamical systems 1982 $\bold{2}$, 195-202, that says that the necessary condition on the periodic points of $X$ and $Y$ for the existence of an embedding of $X$ into $Y$ is also sufficient for the existence of an embedding of $X$ into $Y$. In this note we point out that this theorem extends to certain classes of sofic shifts as target shifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the subsystems of certain sofic shifts Krieger, Wolfgang Dynamical Systems 37B10 For an aperiodic subshift of finite type $Y$ and for a subshift $X$ with topological entropy less than the topological entropy of $Y$, a theorem is proved in Krieger: On the subsystems of topological Markov chains, Ergodic Theory \& dynamical systems 1982 $\bold{2}$, 195-202, that says that the necessary condition on the periodic points of $X$ and $Y$ for the existence of an embedding of $X$ into $Y$ is also sufficient for the existence of an embedding of $X$ into $Y$. In this note we point out that this theorem extends to certain classes of sofic shifts as target shifts. |
| title | On the subsystems of certain sofic shifts |
| topic | Dynamical Systems 37B10 |
| url | https://arxiv.org/abs/2507.02717 |