Geodesic
On multiplicatively dependent linear numeration systems, and periodic points
Frougny, Christiane1 
1 Université Paris 7 LIAFA, UMR 7089 CNRS 2 place Jussieu 75251 Paris Cedex 05 (France) and Université Paris 8
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 3, pp. 293-314

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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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     title = {On multiplicatively dependent linear numeration systems, and periodic points},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {293--314},
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Frougny, Christiane. On multiplicatively dependent linear numeration systems, and periodic points. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 3, pp. 293-314. doi: 10.1051/ita:2002015

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