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A Dynamical Proof of Pisot's Theorem

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Published:2006-03-01
Printed: Mar 2006
• Jaroslaw Kwapisz
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Abstract

We give a geometric proof of classical results that characterize Pisot numbers as algebraic $\lambda>1$ for which there is $x\neq0$ with $\lambda^nx \to 0 \mod$ and identify such $x$ as members of $\Z[\lambda^{-1}] \cdot \Z[\lambda]^*$ where $\Z[\lambda]^*$ is the dual module of $\Z[\lambda]$.
 MSC Classifications: 11R06 - PV-numbers and generalizations; other special algebraic numbers; Mahler measure

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