Digital expansions with negative real bases
Dynamical Systems
2013-11-21 v1 Number Theory
Abstract
Similarly to Parry's characterization of -expansions of real numbers in real bases , Ito and Sadahiro characterized digital expansions in negative bases, by the expansions of the endpoints of the fundamental interval. Parry also described the possible expansions of 1 in base . In the same vein, we characterize the sequences that occur as -expansion of for some . These sequences also describe the itineraries of 1 by linear mod one transformations with negative slope.
Cite
@article{arxiv.1112.1183,
title = {Digital expansions with negative real bases},
author = {Wolfgang Steiner},
journal= {arXiv preprint arXiv:1112.1183},
year = {2013}
}