On the limit points of the fractional parts of powers of Pisot numbers
Dubickas, Artūras
Archivum Mathematicum, Tome 042 (2006), p. 151-158 / Harvested from 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.

Publié le : 2006-01-01
Classification:  11J71,  11R06 
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     author = {Art\=uras Dubickas},
     title = {On the limit points of the fractional parts of powers of Pisot numbers},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {151-158},
     zbl = {1164.11026},
     mrnumber = {2240352},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107991}
}

Dubickas, Artūras. On the limit points of the fractional parts of powers of Pisot numbers. Archivum Mathematicum, Tome 042 (2006) pp. 151-158. http://gdmltest.u-ga.fr/item/107991/

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