A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts always admit characteristic measures. We use similar techniques to show that automorphism groups of minimal zero entropy shifts are sofic.

中文翻译：

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符号动力系统的特征量度

如果概率测度对于系统的自同构群是不变的，则它是拓扑动力系统的特征测度。我们表明，零熵变化总是允许特征度量。我们使用类似的技术来证明最小零熵位移的自同构群是sofic 的。