English

Digital expansions with negative real bases

Dynamical Systems 2013-11-21 v1 Number Theory

Abstract

Similarly to Parry's characterization of β\beta-expansions of real numbers in real bases β>1\beta > 1, 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 β>1\beta > 1. In the same vein, we characterize the sequences that occur as (β)(-\beta)-expansion of ββ+1\frac{-\beta}{\beta+1} for some β>1\beta > 1. 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}
}
R2 v1 2026-06-21T19:46:56.285Z