THE AUTOMORPHISM GROUP OF A SHIFT OF SUBQUADRATIC GROWTH
THE AUTOMORPHISM GROUP OF A SHIFT OF SUBQUADRATIC GROWTH
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DOI：
10.1090/proc12719
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发表时间：
2016-02-01
影响因子：
1
通讯作者：
Kra, Bryna
中科院分区：
文献类型：
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作者：
Cyr, Van;Kra, Bryna
对于有限字母表上的子移位，通过计数长度为n的非空圆柱集的数目来获得系统复杂性的度量。当这种复杂性呈指数级增长时，自同构群对于各种类型的子移位都很大。相反，我们证明了复杂性的次二次增长意味着对于拓扑传递移位X，自同构群Aut（X）是小的：如果H是由移位生成的Aut（X）的子群，则Aut（X）/H是周期的。对于线性增长，我们证明了Aut（X）/H是有限指数群的更强结果.
For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length n. When this complexity grows exponentially, the automorphism group has been shown to be large for various classes of subshifts. In contrast, we show that subquadratic growth of the complexity implies that for a topologically transitive shift X, the automorphism group Aut(X) is small: if H is the subgroup of Aut(X) generated by the shift, then Aut(X)/H is periodic. For linear growth, we show the stronger result that Aut(X)/H is a group of finite exponent.