Abstract
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.
Citation
Masamichi Yoshida. Fumichika Takamizo. "Finite $\beta$-expansion and odometers." Tsukuba J. Math. 45 (2) 135 - 162, December 2021. https://doi.org/10.21099/tkbjm/20214502135
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