Bounded rank-one transformations
Dynamical Systems
2013-09-10 v1
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.
Keywords
Cite
@article{arxiv.1309.1855,
title = {Bounded rank-one transformations},
author = {Su Gao and Aaron Hill},
journal= {arXiv preprint arXiv:1309.1855},
year = {2013}
}