论文标题
诱发的群体作用的相对统一的正熵
Relative uniformly positive entropy of induced amenable group actions
论文作者
论文摘要
Let $G$ be a countable infinite discrete amenable group.It should be noted that a $G$-system $(X,G)$ naturally induces a $G$-system $(\mathcal{M}(X),G)$, where $\mathcal{M}(X)$ denotes the space of Borel probability measures on the compact metric space $X$ endowed with the弱* - 血统。一个因子映射$π\ colon（x，g）\ to（y，g）$在两个$ g $ - 系统之间诱导因子图$ \widetildeπ\ colon（\ Mathcal {m}（m}（x），g），g），to（\ natercal {mathcal {m}（m}（y）（y），g）$。事实证明，只有$ \widetildeπ$开放，并且仅当$π$打开时。当$ y $得到充分支持时，显示出$π$具有相对均匀的正熵，并且仅当$ \ \ \widetildeπ$具有相对均匀的正熵。
Let $G$ be a countable infinite discrete amenable group.It should be noted that a $G$-system $(X,G)$ naturally induces a $G$-system $(\mathcal{M}(X),G)$, where $\mathcal{M}(X)$ denotes the space of Borel probability measures on the compact metric space $X$ endowed with the weak*-topology. A factor map $π\colon (X,G)\to(Y,G)$ between two $G$-systems induces a factor map $\widetildeπ\colon(\mathcal{M}(X),G)\to(\mathcal{M}(Y),G)$. It turns out that $\widetildeπ$ is open if and only if $π$ is open. When $Y$ is fully supported, it is shown that $π$ has relative uniformly positive entropy if and only if $\widetildeπ$ has relative uniformly positive entropy.
