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A Dynamical Proof of Pisot's Theorem
Published online by Cambridge University Press: 20 November 2018
Abstract
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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 
$\mathbb{Z}\left[ \text{ }\!\!\lambda\!\!\text{ } \right]$.
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- Research Article
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- Copyright © Canadian Mathematical Society 2006
References
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