Minimal dynamical systems and approximate conjugacy
Minimal dynamical systems and approximate conjugacy
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DOI：
10.1007/s00208-005-0654-2
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发表时间：
2004-02
影响因子：
1.4
通讯作者：
Huaxin Lin;H. Matui
中科院分区：
文献类型：
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作者：
Huaxin Lin;H. Matui
介绍了极小动力系统的几种近似共轭形式。讨论了近似共轭与相应的交积代数之间的关系。对于康托极小系统，通过ak -理论和c *-代数给出了这些关系的完整描述。例如，当且仅当两个康托极小系统轨道等效且具有相同的周期谱时，它们是近似τ共轭的。还证明了两个这样的系统是近似k共轭的当且仅当对应的交叉积c *-代数具有相同的尺度有序k理论。因此，当且仅当相关变换c *代数同构时，两个康托极小系统是近似k共轭的。顺便说一句，这种近似的k -共轭性与Giordano， Putnam和Skau关于康托极小系统的强轨道等价一致。
Several versions of approximate conjugacy for minimal dynamical systems are introduced. Relation between approximate conjugacy and corresponding crossed productC*-algebras is discussed. For the Cantor minimal systems, a complete description is given for these relations viaK-theory andC*-algebras. For example, it is shown that two Cantor minimal systems are approximatelyτ-conjugate if and only if they are orbit equivalent and have the same periodic spectrum. It is also shown that two such systems are approximatelyK-conjugate if and only if the corresponding crossed productC*-algebras have the same scaled orderedK-theory. Consequently, two Cantor minimal systems are approximatelyK-conjugate if and only if the associated transformationC*-algebras are isomorphic. Incidentally, this approximateK-conjugacy coincides with Giordano, Putnam and Skau’s strong orbit equivalence for the Cantor minimal systems.