论文标题
本地$ \ MATHCAL {P} $熵和稳定的suiphifts subshifts
Local $\mathcal{P}$ entropy and stabilized automorphism groups of subshifts
论文作者
论文摘要
对于同构$ t \ colon x \ to x $ x $的x $ $ x $，稳定的自动形态群体$ \ text {aut}^{（\ infty）}（t）$由所有$ x $的自我塑料组成，这些$ x $均以$ t $ $ t $的电力。在有限类型的转变的背景下，通过研究这些组的研究，我们引入了一种称为本地$ \ Mathcal {p} $熵的组的熵。我们表明，当$（x，t）$是有限类型的非平凡混合转移时，该组$ \ text {aut}^{（\ infty）}（t）的本地$ \ mathcal {p} $熵是由$（x，x，t）$确定的。我们使用它来对稳定的自动形态的同构类型进行完整的分类。
For a homeomorphism $T \colon X \to X$ of a compact metric space $X$, the stabilized automorphism group $\text{Aut}^{(\infty)}(T)$ 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 $\text{Aut}^{(\infty)}(T)$ 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.
