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Issue RAIRO-Theor. Inf. Appl.
Volume 36, Number 3, July-September 2002
Page(s) 293 - 314
DOI 10.1051/ita:2002015

Theoret. Informatics Appl. 36, 293-314 (2002)
DOI: 10.1051/ita:2002015

On multiplicatively dependent linear numeration systems, and periodic points

Christiane Frougny1, 2

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


(Received March, 2002. Accepted October, 2002.)

Abstract
Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers $\beta$ and $\gamma$ respectively, such that $\beta$ and $\gamma$ 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.


Mathematics Subject Classification. 11A63, 11A67, 11B39, 37B10, 68R15

Key words: Numeration system -- Pisot number -- finite automaton -- periodic point.


© EDP Sciences 2002


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