流视图与可识别替换的无限区间交换变换
Flow views and infinite interval exchange transformations for recognizable substitutions
AI总结：
本文提出流视图概念，将替换子移位与无限区间交换变换通过可测共轭联系，证明对偶替换可保证自相似性，并讨论谱类型意义，附常长度替换的谱结果。
摘要：
流视图是可测共轭 $Φ$ 的图形，该共轭将替换或 S-adic 子移位 $(Σ,σ, μ)$ 与 $([0,1], F, m)$ 中无限多个区间的交换联系起来，其中 $m$ 是勒贝格测度。利用规范寻址方案、固定的对偶替换和移位不变概率测度 $μ$，将 $Σ$ 的自然细化分割序列转移到 $([0,1],m)$ 上。在流视图中，$T \in Σ$ 以 $Φ(T)$ 的高度水平显示，使用彩色单位区间表示字母。无限区间交换变换 $F$ 可以被有限多个区间的交换很好地近似，这使得数值和图形方法成为可能。我们证明在某些情况下，对偶替换的选择保证了 $F$ 是自相似的。我们讨论了为什么 $Φ\in L^2(Σ, μ)$ 的谱类型特别值得关注。作为实用性示例，我们包含了一些常长度替换的谱结果。
英文摘要：
A flow view is the graph of a measurable conjugacy $Φ$ between a substitution or S-adic subshift $(Σ,σ, μ)$ and an exchange of infinitely many intervals in $([0,1], F, m)$, where $m$ is Lebesgue measure. A natural refining sequence of partitions of $Σ$ is transferred to $([0,1],m)$ using a canonical addressing scheme, a fixed dual substitution, and a shift-invariant probability measure $μ$. On the flow view, $T \in Σ$ is shown horizontally at a height of $Φ(T)$ using colored unit intervals to represent the letters. The infinite interval exchange transformation $F$ is well approximated by exchanges of finitely many intervals, making numeric and graphic methods possible. We prove that in certain cases a choice of dual substitution guarantees that $F$ is self-similar. We discuss why the spectral type of $Φ\in L^2(Σ, μ),$ is of particular interest. As an example of utility, some spectral results for constant-length substitutions are included.
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