论文标题
比较属性的嵌入定理，用于对符合人群的换档
An embedding theorem for subshifts over amenable groups with the comparison property
论文作者
论文摘要
我们获得以下符号动力系统定理的嵌入定理。让$ g $是一个可数的符合比较属性的可数符合的群体。让$ x $成为超过$ g $的强烈的临时subfrift。让$ y $是有限类型的$ g $上没有全球时期的强烈不可约的转移，这意味着轮班行动对$ y $是忠实的。如果$ x $的拓扑熵严格少于$ y $，而$ y $至少包含$ x $的一个因子，则$ x $嵌入到$ y $中。当$ g = \ mathbb {z} $和Lightwood的结果时，此结果部分扩展了Krieger的经典结果，当$ G = \ Mathbb {z}^d $ for $ d \ geq 2 $时。证据依赖于斜利和准倾斜群体理论的最新发展。
We obtain the following embedding theorem for symbolic dynamical systems. Let $G$ be a countable amenable group with the comparison property. Let $X$ be a strongly aperiodic subshift over $G$. Let $Y$ be a strongly irreducible shift of finite type over $G$ which has no global period, meaning that the shift action is faithful on $Y$. If the topological entropy of $X$ is strictly less than that of $Y$, and $Y$ contains at least one factor of $X$, then $X$ embeds into $Y$. This result partially extends the classical result of Krieger when $G = \mathbb{Z}$ and the results of Lightwood when $G = \mathbb{Z}^d$ for $d \geq 2$. The proof relies on recent developments in the theory of tilings and quasi-tilings of amenable groups.
