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arXiv · 1604.02597

A Family of Totally Rank One Two-sided Shift Maps

Yue Wu·Dongmei Li·Yunjian Wang·Diquan Li
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Abstract

'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.

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Yue Wu, Dongmei Li, Yunjian Wang, Diquan Li. 2016-04-09. A Family of Totally Rank One Two-sided Shift Maps. https://arxiv.org/abs/1604.02597

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