Local $mathcal{P}$ entropy and stabilized automorphism groups of subshifts
Local $mathcal{P}$ entropy and stabilized automorphism groups of subshifts
复制标题
局部 $mathcal{P}$ 熵和子移的稳定自同构群
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
S. Schmieding
中科院分区：
文献类型：
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作者：
S. Schmieding
对于同胚$T冒号X o紧度量空间$X$的X$，稳定自同构群$ ext{Aut}^{（infty）}（T）$由$X$的所有自同胚组成，这些自同胚与$T$的某个幂可交换。出于研究这些群体的背景下，有限型的移位，我们引入了一定的熵群称为本地$mathcal{P}$熵。本文证明了当$（X，T）$是有限型非平凡混合移位时，群$的局部数学熵{P}$ ext{Aut}^{（infty）}（T）$由$（X，T）$的拓扑熵确定。利用这一点，我们给出了全移位的稳定化自同构群的同构类型的一个完全分类。
For a homeomorphism $T colon X o X$ of a compact metric space $X$, the stabilized automorphism group $ ext{Aut}^{(infty)}(T)$ consists of all self-homeomorphisms of $X$ which commute with some power of $T$. Motivated by the study of these groups in the context of shifts of finite type, we introduce a certain entropy for groups called local $mathcal{P}$ entropy. We show that when $(X,T)$ is a non-trivial mixing shift of finite type, the local $mathcal{P}$ entropy of the group $ ext{Aut}^{(infty)}(T)$ is determined by the topological entropy of $(X,T)$. We use this to give a complete classification of the isomorphism type of the stabilized automorphism groups of full shifts.
影响因子：
1
作者：
Hartman, Yair;Kra, Bryna;Schmieding, Scott
通讯作者：
Schmieding, Scott