Isomorphisms between positive and negative beta-transformations
Dynamical Systems
2019-02-20 v1
Abstract
We compare a piecewise linear map with constant slope beta>1 and a piecewise linear map with constant slope -beta. These maps are called the positive and negative beta-transformations. We show that for a certain set of beta's, the multinacci numbers, there exists a measurable isomorphism between these two maps. We further show that for for all other values of beta between 1 and 2 the two maps cannot be isomorphic.
Cite
@article{arxiv.1203.4695,
title = {Isomorphisms between positive and negative beta-transformations},
author = {Charlene Kalle},
journal= {arXiv preprint arXiv:1203.4695},
year = {2019}
}
Comments
18 pages, 8 figures