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On multiplicatively dependent linear numeration systems, and periodic points
Published online by Cambridge University Press: 15 December 2002
Abstract
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.
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- © EDP Sciences, 2002