On multiplicatively dependent linear numeration systems, and periodic points
LIAFA, UMR 7089 du CNRS,
2 place Jussieu,
75251 Paris Cedex 05, France; Christiane.Frougny@liafa.jussieu.fr.
2 Université Paris 8, France
Accepted: October 2002
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.
Mathematics Subject Classification: 11A63 / 11A67 / 11B39 / 37B10 / 68R15
Key words: Numeration system / Pisot number / finite automaton / periodic point.
© EDP Sciences, 2002