On multiplicatively dependent linear numeration systems, and periodic points
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 36 (2002) no. 3, pp. 293-314.

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.

DOI: 10.1051/ita:2002015
Classification: 11A63,  11A67,  11B39,  37B10,  68R15
Keywords: numeration system, Pisot number, finite automaton, periodic point
Frougny, Christiane 1

1 Université Paris 7 LIAFA, UMR 7089 CNRS 2 place Jussieu 75251 Paris Cedex 05 (France) and Université Paris 8
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Frougny, Christiane. On multiplicatively dependent linear numeration systems, and periodic points. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 36 (2002) no. 3, pp. 293-314. doi : 10.1051/ita:2002015. http://www.numdam.org/articles/10.1051/ita:2002015/

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