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On multiplicatively dependent linear numeration systems, and periodic points

Published online by Cambridge University Press:  15 December 2002

Christiane Frougny
Christiane Frougny*
Affiliation:
LIAFA, UMR 7089 du CNRS, 2 place Jussieu, 75251 Paris Cedex 05, France; Christiane.Frougny@liafa.jussieu.fr. Université Paris 8, France
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Abstract

Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers β and γ respectively, such that β and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.

Keywords

Numeration systemPisot numberfinite automatonperiodic point.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 3 , July 2002 , pp. 293 - 314
Copyright
© EDP Sciences, 2002

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