线性模1变换的轨道表示
Orbit Representations from Linear mod 1 Transformations
摘要：
我们发现，每一个点$x_0\in [0,1]$进行一个表示的$C^*$ -代数编码的轨道结构的线性模1区间映射$f_{β,α}(x)=βx +α$。这样的$C^*$ -代数是由部分等距产生的单调的基本映射$f_{β,α}$的子区间。然后我们证明了这种表示是不可约的。此外，对于每个$α\in [0,1[$和$β\geq 1$，两个这样的表示是酉等价的当且仅当点属于同一广义轨道.
英文摘要：
We show that every point $x_0\in [0,1]$ carries a representation of a $C^*$-algebra that encodes the orbit structure of the linear mod 1 interval map $f_{β,α}(x)=βx +α$. Such $C^*$-algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map $f_{β,α}$. Then we prove that such representation is irreducible. Moreover two such of representations are unitarily equivalent if and only if the points belong to the same generalized orbit, for every $α\in [0,1[$ and $β\geq 1$.
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。
