Bounded rank-one transformations

Abstract

We define the notion of canonical boundedness among rank-one transformations and use it to characterize the class of all bounded rank-one transformations with trivial centralizer. We also explicitly characterize totally ergodic rank-one transformations with bounded cutting parameter. Together with a recent result of Ryzhikov our results provide a simple procedure for determining whether a bounded rank-one transformation has minimal self-joinings of all orders purely in terms of the cutting and spacer parameters for the transformation.

References in corpus (3)

• Minimal Self-Joinings, Bounded Constructions, and Weak Closure of Ergodic Actions
• On the correlation of the Moebius function with random rank-one systems
• Weak mixing of maps with bounded cutting parameter