Some results on the classification of expansive automorphisms of compact abelian groups
Some results on the classification of expansive automorphisms of compact abelian groups
复制标题
紧阿贝尔群的扩张自同构分类的一些结果
DOI：
10.1017/s0143385700008701
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发表时间：
1996
影响因子：
0.9
通讯作者：
F. Fagnani
中科院分区：
文献类型：
--
作者：
F. Fagnani
摘要本文研究了紧0维交换群的扩张自同构。我们的主要结果是完整的代数和拓扑分类的传递扩张自同构的元素的最大阶为p2的一个素数p。这产生一个分类的传递扩张自同构的拓扑熵log p2。最后，我们证明了有限群上的可扩自同构在拓扑上和代数上与移位共轭的一个充要条件。
Abstract In this paper we study expansive automorphisms of compact 0-dimensional abelian groups. Our main result is the complete algebraic and topological classification of the transitive expansive automorpisms for which the maximal order of the elements is p2 for a prime p. This yields a classification of the transitive expansive automorphisms with topological entropy log p2. Finally, we prove a necessary and sufficient condition for an expansive automorphism to be conjugated, topologically and algebraically, to a shift over a finite group.