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Dynamical Directions in Numeration

Abstract : 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.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00130853
Contributor : Valerie Berthe <>
Submitted on : Tuesday, February 27, 2007 - 11:46:18 AM
Last modification on : Wednesday, April 1, 2020 - 12:20:06 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 11:54:32 PM

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  • HAL Id : lirmm-00130853, version 1

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Valerie Berthe, Guy Barat, Jorg Thuswaldner, Pierre Liardet. Dynamical Directions in Numeration. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2006, 56, pp.1987-2092. ⟨lirmm-00130853⟩

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