<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

Published Online: Jan 13, 2017

Page range: 175 - 186

Received: Apr 14, 2016

Accepted: Apr 26, 2016

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

Keywords
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

Published Online: Jan 13, 2017

Page range: 175 - 186

Received: Apr 14, 2016

Accepted: Apr 26, 2016

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

Keywordsbeta-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.

Keywords
beta-expansions, odometer, purely discrete spectrum, finiteness property