Rank-One Transformations, Odometers, and Finite Factors
Dynamical Systems
2021-06-18 v3
Abstract
In this paper we give explicit characterizations, based on the cutting and spacer parameters, of (a) which rank-one transformations factor onto a given finite cyclic permutation, (b) which rank-one transformations factor onto a given odometer, and (c) which rank-one transformations are isomorphic to a given odometer. These naturally yield characterizations of (d) which rank-one transformations factor onto some (unspecified) finite cyclic permutation, (d') which rank-one transformations are totally ergodic, (e) which rank-one transformations factor onto some (unspecified) odometer, and (f) which rank-one transformations are isomorphic to some (unspecified) odometer.
Keywords
Cite
@article{arxiv.1910.12645,
title = {Rank-One Transformations, Odometers, and Finite Factors},
author = {Matthew Foreman and Su Gao and Aaron Hill and Cesar E. Silva and Benjamin Weiss},
journal= {arXiv preprint arXiv:1910.12645},
year = {2021}
}