Geodesic
On the limit points of the fractional parts of powers of Pisot numbers
Archivum mathematicum, Tome 42 (2006) no. 2, pp. 151-158 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We consider the sequence of fractional parts $\lbrace \xi \alpha ^n\rbrace $, $n=1,2,3,\dots $, where $\alpha >1$ is a Pisot number and $\xi \in {\mathbb Q}(\alpha )$ is a positive number. We find the set of limit points of this sequence and describe all cases when it has a unique limit point. The case, where $\xi =1$ and the unique limit point is zero, was earlier described by the author and Luca, independently.
We consider the sequence of fractional parts $\lbrace \xi \alpha ^n\rbrace $, $n=1,2,3,\dots $, where $\alpha >1$ is a Pisot number and $\xi \in {\mathbb Q}(\alpha )$ is a positive number. We find the set of limit points of this sequence and describe all cases when it has a unique limit point. The case, where $\xi =1$ and the unique limit point is zero, was earlier described by the author and Luca, independently.
Classification : 11J71, 11R06
Keywords: Pisot numbers; fractional parts; limit points 
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Dubickas, Artūras. On the limit points of the fractional parts of powers of Pisot numbers. Archivum mathematicum, Tome 42 (2006) no. 2, pp. 151-158. http://geodesic.mathdoc.fr/item/ARM_2006_42_2_a5/

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