Finite $\beta$-expansion and odometers
Masamichi Yoshida, Fumichika Takamizo · Tsukuba Journal of Mathematics · 2021
Let $\beta > 1$. In this paper, we define the odometer associated with a $\beta$-numeration system, and study its properties. As a result, we characterize the finiteness or positive finiteness property of this numeration system by using this odometer. We also study the computability of this odometer via natural transducer.