Dynamical directions in numeration

Guy Barat[1]; Valérie Berthé[2]; Pierre Liardet[3]; Jörg Thuswaldner[4]

  • [1] Institut für Mathematik A T.U. Graz - Steyrergasse 30 8010 Graz (Austria)
  • [2] Université Montpellier II LIRMM — CNRS UMR 5506 161 rue Ada 34392 Montpellier Cedex 5 (France)
  • [3] Université de Provence CMI- 39 rue Joliot-Curie 13453 Marseille Cedex 13 (France)
  • [4] Montan Universtät Leoben Chair of Mathematics and Statistics Franz-Josef-Straße 18 8700 Leoben (Austria)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 7, page 1987-2092
  • ISSN: 0373-0956


This survey aims at giving a consistent presentation of numeration from a dynamical viewpoint: we focus on numeration systems, their associated compactification, and dynamical systems that can be naturally defined on them. The exposition is unified by the fibred numeration system concept. Many examples are discussed. Various numerations on rational integers, real or complex numbers are presented with special attention paid to β -numeration and its generalisations, abstract numeration systems and shift radix systems, as well as G -scales and odometers. A section of applications ends the paper.

How to cite


Barat, Guy, et al. "Dynamical directions in numeration." Annales de l’institut Fourier 56.7 (2006): 1987-2092. <http://eudml.org/doc/10197>.

abstract = {This survey aims at giving a consistent presentation of numeration from a dynamical viewpoint: we focus on numeration systems, their associated compactification, and dynamical systems that can be naturally defined on them. The exposition is unified by the fibred numeration system concept. Many examples are discussed. Various numerations on rational integers, real or complex numbers are presented with special attention paid to $\beta $-numeration and its generalisations, abstract numeration systems and shift radix systems, as well as $G$-scales and odometers. A section of applications ends the paper.},
affiliation = {Institut für Mathematik A T.U. Graz - Steyrergasse 30 8010 Graz (Austria); Université Montpellier II LIRMM — CNRS UMR 5506 161 rue Ada 34392 Montpellier Cedex 5 (France); Université de Provence CMI- 39 rue Joliot-Curie 13453 Marseille Cedex 13 (France); Montan Universtät Leoben Chair of Mathematics and Statistics Franz-Josef-Straße 18 8700 Leoben (Austria)},
author = {Barat, Guy, Berthé, Valérie, Liardet, Pierre, Thuswaldner, Jörg},
journal = {Annales de l’institut Fourier},
keywords = {Numeration; fibred systems; symbolic dynamics; odometers; numeration scales; subshifts; $f$-expansions; $\beta $-numeration; sum-of-digits function; abstract number systems; canonical numeration systems; shift radix systems; additive functions; tilings; Rauzy fractals; substitutive dynamical systems; bibliography; numeration; -expansions; -numeration},
language = {eng},
number = {7},
pages = {1987-2092},
publisher = {Association des Annales de l’institut Fourier},
title = {Dynamical directions in numeration},
url = {http://eudml.org/doc/10197},
volume = {56},
year = {2006},

AU - Barat, Guy
AU - Berthé, Valérie
AU - Liardet, Pierre
AU - Thuswaldner, Jörg
TI - Dynamical directions in numeration
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 7
SP - 1987
EP - 2092
AB - This survey aims at giving a consistent presentation of numeration from a dynamical viewpoint: we focus on numeration systems, their associated compactification, and dynamical systems that can be naturally defined on them. The exposition is unified by the fibred numeration system concept. Many examples are discussed. Various numerations on rational integers, real or complex numbers are presented with special attention paid to $\beta $-numeration and its generalisations, abstract numeration systems and shift radix systems, as well as $G$-scales and odometers. A section of applications ends the paper.
LA - eng
KW - Numeration; fibred systems; symbolic dynamics; odometers; numeration scales; subshifts; $f$-expansions; $\beta $-numeration; sum-of-digits function; abstract number systems; canonical numeration systems; shift radix systems; additive functions; tilings; Rauzy fractals; substitutive dynamical systems; bibliography; numeration; -expansions; -numeration
UR - http://eudml.org/doc/10197
ER -


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