The automorphism group of a minimal shift of stretched exponential growth
The automorphism group of a minimal shift of stretched exponential growth
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拉伸指数增长的最小平移的自同构群
DOI：
10.3934/jmd.2016.10.483
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Bryna Kra
中科院分区：
文献类型：
--
作者：
Van Cyr;Bryna Kra
符号动力系统的自同构群是可数的，但通常非常大。例如，对于有限类型的混合子移，自同构群包含两个生成器上自由群的同构副本以及 $\mathbb{Z}$ 的可数个副本的直和。相比之下，零熵符号系统的自同构群似乎受到高度约束。我们的主要结果是，指数 $<1/2$ 的拉伸指数增长的任何最小子移的自同构群是可以接受的（作为可数离散群）。对于多项式增长的移位，我们进一步证明 Aut(X) 的任何有限生成的无挠子群实际上是幂零的。
The group of automorphisms of a symbolic dynamical system is countable, but often very large. For example, for a mixing subshift of finite type, the automorphism group contains isomorphic copies of the free group on two generators and the direct sum of countably many copies of $\mathbb{Z}$. In contrast, the group of automorphisms of a symbolic system of zero entropy seems to be highly constrained. Our main result is that the automorphism group of any minimal subshift of stretched exponential growth with exponent $<1/2$, is amenable (as a countable discrete group). For shifts of polynomial growth, we further show that any finitely generated, torsion free subgroup of Aut(X) is virtually nilpotent.