THE AUTOMORPHISM GROUP OF A SHIFT OF LINEAR GROWTH: BEYOND TRANSITIVITY
THE AUTOMORPHISM GROUP OF A SHIFT OF LINEAR GROWTH: BEYOND TRANSITIVITY
复制标题
线性增长平移的自同构群：超越传递性
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Bryna Kra
中科院分区：
文献类型：
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作者：
Van Cyr;Bryna Kra
对于因子复杂度函数最大线性增长的有限字母${mathcal{a}}$和移位$Xsubseteq {mathcal{a}}^{mathbb{Z}}$，研究了自同构群$ ext{Aut}(X)$的代数性质。对于这样的系统，我们证明了$ ext{Aut}(X)$的每个有限生成的子群实际上是$mathbb{Z}^{d}$，这与复杂性函数增长更快时的行为形成了对比。通过附加的动态假设，我们展示了更多：如果$X$是可传递的，那么$ ext{Aut}(X)$实际上是$mathbb{Z}$；如果$X$有密集的非周期点，则$ ext{Aut}(X)$实际上是$mathbb{Z}^{d}$。我们还对所有作为移位的自同构群出现的有限群进行了分类。
For a finite alphabet ${mathcal{A}}$ and shift $Xsubseteq {mathcal{A}}^{mathbb{Z}}$ whose factor complexity function grows at most linearly, we study the algebraic properties of the automorphism group $ ext{Aut}(X)$. For such systems, we show that every finitely generated subgroup of $ ext{Aut}(X)$ is virtually $mathbb{Z}^{d}$, in contrast to the behavior when the complexity function grows more quickly. With additional dynamical assumptions we show more: if $X$ is transitive, then $ ext{Aut}(X)$ is virtually $mathbb{Z}$; if $X$ has dense aperiodic points, then $ ext{Aut}(X)$ is virtually $mathbb{Z}^{d}$. We also classify all finite groups that arise as the automorphism group of a shift.