Toeplitz 移位拓扑分解的障碍
Obstacles to Topological Factoring of Toeplitz shifts
AI总结：
针对Toeplitz移位的拓扑分解问题，利用构造性周期结构及Bratteli-Vershik表示，证明存在拓扑分解时构造性周期结构满足整除关系，共轭时结构相等，并证实Toeplitz序列经分解仍为Toeplitz序列。
摘要：
对于每个具有周期结构$(q_i)_{i\geq 1}$的Toeplitz序列$x$，可确定一个周期结构${\bf p}=(p_i)_{i\geq 0}$，该结构能实现相关Toeplitz移位的Bratteli-Vershik表示；我们称此周期结构为“构造性”的。设$(X,σ,x)$和$(Y,σ,y)$为Toeplitz移位，其中$x\in X$和$y\in Y$是具有构造性周期结构$(p^n)_{n\geq 1}$和$(q^n)_{n\geq 1}$的Toeplitz序列。利用Toeplitz移位间因子映射的Bratteli-Vershik表示，我们证明：若存在拓扑分解$π:(X,σ)\rightarrow(Y,σ)$满足$π(x)=y$，则$q\mid p$；特别地，若$π$是共轭，则$p=q$。我们还证明Toeplitz序列通过拓扑分解可映射为Toeplitz序列。
英文摘要：
For every Toeplitz sequence $x$ with period structure $(q_i)_{i\geq 1}$, one can identify a period structure ${\bf p}=(p_i)_{i\geq 0}$ which leads to a Bratteli-Vershik realization of the associated Toeplitz shift; we refer to this period structure as {\it constructive}. Let $(X,σ,x)$ and $(Y,σ,y)$ be Toeplitz shifts where $x\in X$ and $y\in Y$ are Toeplitz sequences with constructive period structures $(p^n)_{n\geq 1}$ and $(q^n)_{n\geq 1}$, respectively. Using the Bratteli-Vershik realization of factor maps between Toeplitz shifts, we prove that if there exists a topological factoring $ π:(X,σ)\rightarrow (Y,σ)$ with $π(x)=y$, then $q\mid p$. In particular, if $π$ is conjugacy, then $p=q$. We also prove that Toeplitz sequences are mapped to Toeplitz sequences through topological factorings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
