Acta Mathematica Hungarica

, Volume 139, Issue 1–2, pp 106–119 | Cite as

Digital expansions with negative real bases



Similarly to Parry’s characterization of β-expansions of real numbers in real bases β>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. In the same way, we characterize the sequences that occur as (−β)-expansion of \(\frac{-\beta}{\beta+1}\) for some β>1. These sequences also describe the itineraries of 1 by linear mod one transformations with negative slope.

Key words and phrases

digital expansion β-expansion β-transformation negative basis 

Mathematics Subject Classification

11A63 37B10 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012

Authors and Affiliations

  1. 1.LIAFA, CNRS UMR 7089Université Paris Diderot – Paris 7Paris Cedex 13France

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