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A Dynamical Proof of Pisot's Theorem

Published online by Cambridge University Press:  20 November 2018

Jaroslaw Kwapisz
Jaroslaw Kwapisz*
Affiliation:
Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717-2400, U.S.A. e-mail: jarek@math.montana.edu
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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 $\mathbb{Z}\left[ \text{ }\!\!\lambda\!\!\text{ } \right]$ .

Keywords

11R06

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 1 , 01 March 2006 , pp. 108 - 112
Copyright
Copyright © Canadian Mathematical Society 2006

References

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