Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866910397462740992 |
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| author | Ceccherini-Silberstein, Tullio Coornaert, Michel Li, Hanfeng |
| author_facet | Ceccherini-Silberstein, Tullio Coornaert, Michel Li, Hanfeng |
| contents | A dynamical system is a pair $(X,G)$, where $X$ is a compact metrizable space and $G$ is a countable group acting by homeomorphisms of $X$. An endomorphism of $(X,G)$ is a continuous selfmap of $X$ which commutes with the action of $G$. One says that a dynamical system $(X,G)$ is surjunctive provided that every injective endomorphism of $(X,G)$ is surjective (and therefore is a homeomorphism). We show that when $G$ is sofic, every expansive dynamical system $(X,G)$ with nonnegative sofic topological entropy and satisfying the weak specification and the strong topological Markov properties, is surjunctive. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2107_12047 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity Ceccherini-Silberstein, Tullio Coornaert, Michel Li, Hanfeng Dynamical Systems Group Theory 37B40, 37B10, 37D20, 20F65 A dynamical system is a pair $(X,G)$, where $X$ is a compact metrizable space and $G$ is a countable group acting by homeomorphisms of $X$. An endomorphism of $(X,G)$ is a continuous selfmap of $X$ which commutes with the action of $G$. One says that a dynamical system $(X,G)$ is surjunctive provided that every injective endomorphism of $(X,G)$ is surjective (and therefore is a homeomorphism). We show that when $G$ is sofic, every expansive dynamical system $(X,G)$ with nonnegative sofic topological entropy and satisfying the weak specification and the strong topological Markov properties, is surjunctive. |
| title | Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity |
| topic | Dynamical Systems Group Theory 37B40, 37B10, 37D20, 20F65 |
| url | https://arxiv.org/abs/2107.12047 |