Geodesic
A Dynamical Proof of Pisot's Theorem
Canadian mathematical bulletin, Tome 49 (2006) no. 1, pp. 108-112

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DOI

We give a geometric proof of classical results that characterize Pisot numbers as algebraic $\text{ }\lambda \,>1$ for which there is $x\ne 0$ with $\text{ }\lambda {{\text{ }}^{n}}x\to 0\left( \,\bmod \,\,1 \right)$ and identify such $x$ as members of $\mathbb{Z}\left[ \text{ }\lambda {{\text{ }}^{-1}} \right]\cdot$ $\mathbb{Z}{{\left[ \text{ }\!\!\lambda\!\!\text{ } \right]}^{*}}$ where $\mathbb{Z}{{\left[ \text{ }\!\!\lambda\!\!\text{ } \right]}^{*}}$ is the dual module of $\mathbb{Z}\left[ \text{ }\!\!\lambda\!\!\text{ } \right]$ .
DOI : 10.4153/CMB-2006-010-9
Mots-clés : 11R06 
Kwapisz, Jaroslaw. A Dynamical Proof of Pisot's Theorem. Canadian mathematical bulletin, Tome 49 (2006) no. 1, pp. 108-112. doi: 10.4153/CMB-2006-010-9
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     author = {Kwapisz, Jaroslaw},
     title = {A {Dynamical} {Proof} of {Pisot's} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {108--112},
     year = {2006},
     volume = {49},
     number = {1},
     doi = {10.4153/CMB-2006-010-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-010-9/}
}
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