Constructive symbolic presentations of rank one measure-preserving systems
Constructive symbolic presentations of rank one measure-preserving systems
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第一级测度保持系统的建设性符号表示
DOI：
10.4064/cm7124-3-2017
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
K. Petersen
中科院分区：
文献类型：
--
作者：
Terrence M. Adams;S. Ferenczi;K. Petersen
给定一个通过切割和堆叠间隔物定义的一级测度保留系统，我们产生一个一级二元序列，使得其在移位变换下的轨道闭合以其独特的{非原子}不变概率与给定系统同构。特别是，经典的二元里程表是根据双符号字母表 $\{0,1\}$ 上的块的递归序列来呈现的。该构造是使用 adic 或 Bratteli-Vershik 系统设置中的第一级定义来完成的。
Given a rank one measure-preserving system defined by cutting and stacking with spacers, we produce a rank one binary sequence such that its orbit closure under the shift transformation, with its unique {nonatomic} invariant probability, is isomorphic to the given system. In particular, the classical dyadic odometer is presented in terms of a recursive sequence of blocks on the two-symbol alphabet $\{0,1\}$. The construction is accomplished using a definition of rank one in the setting of adic, or Bratteli-Vershik, systems.