%0 Journal Article
%T Dynamical Directions in Numeration
%+ Arithmétique informatique (ARITH)
%+ Institut für Mathematik [Graz] (IM)
%+ Montanuniversität Leoben (MUL)
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%A Berthe, Valerie
%A Barat, Guy
%A Thuswaldner, Jorg
%A Liardet, Pierre
%< avec comité de lecture
%@ 0373-0956
%J Annales de l'Institut Fourier
%I Association des Annales de l'Institut Fourier
%V 56
%P 1987-2092
%8 2006
%D 2006
%R 10.5802/aif.2233
%Z Computer Science [cs]/Discrete Mathematics [cs.DM]
%Z Mathematics [math]/Dynamical Systems [math.DS]
%Z Mathematics [math]/Number Theory [math.NT]Journal articles
%X We survey definitions and properties of numeration from a dynamical point of view. That is we focuse on numeration systems, their associated compactifications, and the dynamical systems that can be naturally defined on them. The exposition is unified by the notion of fibred numeration system. A lot of examples are discussed. Various numerations on natural, integral, real or complex numbers are presented with a special attention payed to beta-numeration and its generalisations, abstract numeration systems and shift radix systems. A section of applications ends the paper.
%G English
%2 https://hal-lirmm.ccsd.cnrs.fr/lirmm-00130853/document
%2 https://hal-lirmm.ccsd.cnrs.fr/lirmm-00130853/file/RR06003.pdf
%L lirmm-00130853
%U https://hal-lirmm.ccsd.cnrs.fr/lirmm-00130853
%~ LATP
%~ CNRS
%~ UNIV-AMU
%~ I2M
%~ LIRMM
%~ TDS-MACS
%~ MIPS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021