一类全秩1的双侧移位映射
A Family of Totally Rank One Two-sided Shift Maps
摘要：
引入了广义Chacon映射（\cite{FER1}）的一个子族“广义delJunco-Rudolph映射”.引入了与广义delJunco-Rudolph映射结构有关的斜积。基于此斜积的迭代命题，证明了一个相对素关系$h_{k+1}\equiv 1 \mod q$。如果$T^{q}$对于每个$q\in \mathbb{N}$都是秩1，则我们称保测变换$T$是全秩1的.本文证明了每个广义delJunco-Rudolph映射都是全秩1的。
英文摘要：
'Generalized del Junco-Rudolph's map', a sub-family of generalized Chacon's map (\cite{FER1}), is introduced. A skew product related to the structure of the Generalized del Junco-Rudolph's map is introduced. A Relative Prime Relation, $h_{k+1}\equiv 1 \mod q$ is verified, based on the proposition of iterations of this skew product. We say a measure-preserving transformation $T$ is totally rank one if $T^{q}$ is rank one for every $q\in \mathbb{N}$. In this paper, we show that of every Generalized del Junco-Rudolph's map is totally rank one.
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。
