<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The aim of this paper is to study the connection between different properties related to <italic>β</italic>-expansions. In particular, the relation between two conditions, both ensuring purely discrete spectrum of the odometer, is analyzed. The first one is the so-called Hypothesis B for the <italic>G</italic>-odometers and the second one is denoted by (QM) and it has been introduced in the framework of tilings associated to Pisot <italic>β</italic>-numerations.</p></abstract>

The aim of this paper is to study the connection between different properties related to β-expansions. In particular, the relation between two conditions, both ensuring purely discrete spectrum of the odometer, is analyzed. The first one is the so-called Hypothesis B for the G-odometers and the second one is denoted by (QM) and it has been introduced in the framework of tilings associated to Pisot β-numerations.

Linear Recursive Odometers and Beta-Expansions

maria-rita.iaco@liafa.univ-paris-diderot.fr

IRIF, CNRS UMR 8243, Université Paris Diderot – Paris 7, Case 7014, 75205 Paris Cedex 13,

Graz University of Technology, Institute for Analysis and Number Theory, Steyrergasse 30, 8010 Graz,

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Linear Recursive Odometers and Beta-Expansions"}

The aim of this paper is to study the connection between different properties related to β-expansions. In particular, the relation between two conditions, both...

Linear Recursive Odometers and Beta-Expansions

Publié en ligne: 13 janv. 2017

Pages: 175 - 186

Reçu: 14 avr. 2016

Accepté: 26 avr. 2016

DOI: https://doi.org/10.1515/udt-2016-0010

Mots clés
beta-expansions, odometer, purely discrete spectrum, finiteness property

© 2016 Maria Rita Iacò et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Linear Recursive Odometers and Beta-Expansions

Publié en ligne: 13 janv. 2017

Pages: 175 - 186

Reçu: 14 avr. 2016

Accepté: 26 avr. 2016

DOI: https://doi.org/10.1515/udt-2016-0010

Mots clésbeta-expansions, odometer, purely discrete spectrum, finiteness property

© 2016 Maria Rita Iacò et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
beta-expansions, odometer, purely discrete spectrum, finiteness property