On purely periodic beta-expansions of Pisot numbers

Yuki Sano

doi:nmj/1114631738

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Home > Journals > Nagoya Math. J. > Volume 166 > Article

2002 On purely periodic beta-expansions of Pisot numbers

Yuki Sano

Nagoya Math. J. 166: 183-207 (2002).

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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.