A Family of Totally Rank One Two-sided Shift Maps

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, $h_{k+1}\equiv 1\mathrm{mod}q$ 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.

8 pages

References in corpus (2)

• Several questions and hypotheses concerning the limit polynomials for Chacon transformation
• Totally Rank One Interval Exchange Transformations

Cited by in corpus (1)

• Totally Rank One Interval Exchange Transformations