Abstract
We characterize numbers having purely periodic $\beta$-expansions where $\beta$ is a Pisot number satisfying a certain irreducible polynomial. The main tool of the proof is to construct a natural extension on a $d$-dimensional domain with a fractal boundary.
Citation
Yuki Sano. "On purely periodic beta-expansions of Pisot numbers." Nagoya Math. J. 166 183 - 207, 2002.
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