On multiplicatively dependent linear numeration systems, and periodic points

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

• Type: Journal
• Year: 2002
• Where: ITA
• Authors: Christiane Frougny
• Keywords: Characteristic Polynomial, Communications, ITA 2002, Linear Numeration Systems, Minimal Polynomial