Universality of G-subshifts with specification
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916695769088000 |
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| author | Downarowicz, Tomasz Weiss, Benjamin Więcek, Mateusz Zhang, Guohua |
| author_facet | Downarowicz, Tomasz Weiss, Benjamin Więcek, Mateusz Zhang, Guohua |
| contents | Let $G$ be an infinite countable amenable group and let $(X,G)$ be a $G$-subshift with specification, containing a free element. We prove that $(X,G)$ is universal, i.e., has positive topological entropy and for any free ergodic $G$-action on a standard probability space, $(Y,ν,G)$, with $h(ν)<h_{top}(X)$, there exists a shift-invariant measure $μ$ on $X$ such that the systems $(Y,ν,G)$ and $(X,μ,G)$ are isomorphic. In particular, any $K$-shift (consisting of the indicator functions of all maximal $K$-separated sets) containing a free element is universal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13307 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality of G-subshifts with specification Downarowicz, Tomasz Weiss, Benjamin Więcek, Mateusz Zhang, Guohua Dynamical Systems Primary 37E20, 37A35, Secondary 43A07, 37B40 Let $G$ be an infinite countable amenable group and let $(X,G)$ be a $G$-subshift with specification, containing a free element. We prove that $(X,G)$ is universal, i.e., has positive topological entropy and for any free ergodic $G$-action on a standard probability space, $(Y,ν,G)$, with $h(ν)<h_{top}(X)$, there exists a shift-invariant measure $μ$ on $X$ such that the systems $(Y,ν,G)$ and $(X,μ,G)$ are isomorphic. In particular, any $K$-shift (consisting of the indicator functions of all maximal $K$-separated sets) containing a free element is universal. |
| title | Universality of G-subshifts with specification |
| topic | Dynamical Systems Primary 37E20, 37A35, Secondary 43A07, 37B40 |
| url | https://arxiv.org/abs/2504.13307 |