On topological rank of factors of Cantor minimal systems
On topological rank of factors of Cantor minimal systems
复制标题
康托极小系统因子的拓扑排序
DOI：
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发表时间：
2020
影响因子：
0.9
通讯作者：
Maryam Hosseini
中科院分区：
文献类型：
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作者：
Nasser Golestani;Maryam Hosseini
摘要如果一个Cantor极小系统有一个每层顶点数一致有界的Bratteli-Vershik表示，则它是有限拓扑阶的。证明了如果Cantor集上的极小动力系统的拓扑秩是有限的，那么它的所有极小Cantor因子也都有有限的拓扑秩.这对多诺索、杜兰德、马斯和佩蒂提出的问题给予了肯定的回答。作为结果，我们得到了有限秩康托极小系统的康托因子的Downarowicz和Maass的二分法：它们要么是里程计，要么是子移位。
Abstract A Cantor minimal system is of finite topological rank if it has a Bratteli–Vershik representation whose number of vertices per level is uniformly bounded. We prove that if the topological rank of a minimal dynamical system on a Cantor set is finite, then all its minimal Cantor factors have finite topological rank as well. This gives an affirmative answer to a question posed by Donoso, Durand, Maass, and Petite in full generality. As a consequence, we obtain the dichotomy of Downarowicz and Maass for Cantor factors of finite-rank Cantor minimal systems: they are either odometers or subshifts.