Special homeomorphisms and approximation for Cantor systems
Special homeomorphisms and approximation for Cantor systems
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康托系统的特殊同胚和近似
DOI：
10.1016/j.topol.2013.10.018
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发表时间：
2014
影响因子：
0.6
通讯作者：
T. Shimomura
中科院分区：
文献类型：
--
作者：
T. Shimomura
摘要E. Akin，E. Einner和B。韦斯在所有Cantor同胚空间中构造了一个具有稠密G δ共轭类的特殊同胚。M. Hochman证明了泛里程表是所有拓扑传递的Cantor同胚空间中的特殊同胚。按照E. Akin，E.格拉斯纳和B。韦斯的结果，证明了泛里程表是所有链传递Cantor系统空间中的特殊同胚.我们将这一结果推广到链传递系统的周期谱的限制空间。进一步，我们构造了所有链循环系统空间中的特殊同胚。在这样做时，每个0维系统被描述为有限有向图和图同态序列的逆极限。在前面的文章中，我们证明了一个周期条件决定了一个Cantor系统是否通过拓扑共轭逼近一个链混合Cantor系统。我们将把这个结果推广到链传递的情形。这些条件被描述在序列的有限有向图和图同态。
Abstract E. Akin, E. Glasner, and B. Weiss had constructed the special homeomorphism that has a dense G δ conjugacy class in the space of all Cantor homeomorphisms. M. Hochman showed that the universal odometer is the special homeomorphism in the space of all topologically transitive Cantor homeomorphism. Following the approach of E. Akin, E. Glasner, and B. Weiss, we show that the universal odometer is the special homeomorphism in the space of all chain transitive Cantor systems. We extend this result to the space of chain transitive systems that are restricted by a periodic spectrum. Further, we construct the special homeomorphism in the space of all chain recurrent systems. In doing so, every 0-dimensional system is described as the inverse limit of a sequence of finite directed graphs and graph homomorphisms. In the previous paper, we had shown that a certain periodic condition determines whether a Cantor system approximates a chain mixing Cantor system by topological conjugacies. We shall extend this result to the chain transitive case. These conditions are described in terms of sequences of finite directed graphs and graph homomorphisms.
影响因子：
1.4
作者：
Huaxin Lin;H. Matui
通讯作者：
Huaxin Lin;H. Matui
近似共轭和康托最小系统的完整群
DOI：
--
发表时间：
--
期刊：
Publications of Research Institute for Mathematical Sciences (未定)
影响因子：
--
作者：
Huaxin Lin;松井 宏樹;松井 宏樹
通讯作者：
松井 宏樹