Let $\mathcal {G}$ be a second countable, Hausdorff topological group. If $\mathcal {G}$ is locally compact, totally disconnected and T is an expansive automorphism then it is shown that the dynamical system $(\mathcal {G}, T)$ is topologically conjugate to the product of a symbolic full-shift on a finite number of symbols, a totally wandering, countable-state Markov shift and a permutation of a countable coset space of $\mathcal {G}$ that fixes the defining subgroup. In particular if the automorphism is transitive then $\mathcal {G}$ is compact and $(\mathcal {G}, T)$ is topologically conjugate to a full-shift on a finite number of symbols.

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局部紧群的扩展动态

让$\数学{G}$是第二个可数的 Hausdorff 拓扑群。如果$\数学{G}$是局部紧致的，完全断开的，并且吨是一个扩展的自同构，那么它证明了动力系统$(\mathcal {G}, T)$在拓扑上共轭到有限数量符号上的符号全移位、完全漂移的可数状态马尔可夫移位和可数陪集空间的置换的乘积$\数学{G}$修复了定义子组。特别是如果自同构是传递的，那么$\数学{G}$紧凑且$(\mathcal {G}, T)$拓扑共轭到有限数量符号上的全位移。