Numbers with integer expansion in the system with negative base

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F12%3A00186826" target="_blank" >RIV/68407700:21340/12:00186826 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.7169/facm/2012.47.2.8" target="_blank" >http://dx.doi.org/10.7169/facm/2012.47.2.8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.7169/facm/2012.47.2.8" target="_blank" >10.7169/facm/2012.47.2.8</a>

Result language

angličtina

Original language name

Numbers with integer expansion in the system with negative base

Original language description

In this paper, we study representations of real numbers in the positional numeration system with negative basis, as introduced by Ito and Sadahiro. We focus on the set $Z_{-beta}$ of numbers whose representation uses only non-negative powers of $-beta$, the so-called $(-beta)$-integers. We describe the distances between consecutive elements of $Z_{-beta}$. In case that this set is non-trivial we associate to $beta$ an infinite word $boldsymbol{v}_{-beta}$ over an (in general infinite) alphabet.The self-similarity of $Z_{-beta}$, i.e., the property $-betaZ_{-beta}subset Z_{-beta}$, allows us to find a morphism under which $boldsymbol{v}_{-beta}$ is invariant. On the example of two cubic irrational bases $beta$ we demonstrate the difference between Rauzy fractals generated by $(-beta)$-integers and by $beta$-integers.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Publication year

2012

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Functiones et Approximatio, Commentarii Mathematici

ISSN

0208-6573

e-ISSN

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Volume of the periodical

47

Issue of the periodical within the volume

2

Country of publishing house

PL - POLAND

Number of pages

26

Pages from-to

241-266

UT code for WoS article

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EID of the result in the Scopus database

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