English

Disjointness between bounded rank-one transformations

Dynamical Systems 2016-01-19 v1

Abstract

In this paper some sufficient conditions are given for when two bounded rank-one transformations are isomorphic or disjoint. For commensurate, canonically bounded rank-one transformations, isomorphism and disjointness are completely determined by simple conditions in terms of their cutting and spacer parameters. We also obtain sufficient conditions for bounded rank-one transformations to have minimal self-joinings. As an application, we give a proof of Ryzhikov's theorem that totally ergodic, non-rigid, bounded rank-one transformations have minimal self-joinings of all orders.

Keywords

Cite

@article{arxiv.1601.04119,
  title  = {Disjointness between bounded rank-one transformations},
  author = {Su Gao and Aaron Hill},
  journal= {arXiv preprint arXiv:1601.04119},
  year   = {2016}
}
R2 v1 2026-06-22T12:30:35.919Z