Universality of G-subshifts with specification

Fuente: arXiv
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Autori principali: Downarowicz, Tomasz, Weiss, Benjamin, Więcek, Mateusz, Zhang, Guohua
Natura: Preprint
Pubblicazione: 2025
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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