Isomorphisms between positive and negative beta-transformations
arXiv:1203.4695 · doi:10.1017/etds.2012.127
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.
18 pages, 8 figures