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June 2008 Periodicity of Certain Piecewise Affine Planar Maps
Shigeki Akiyama, Horst Brunotte, Attila Pethö, Wolfgang Steiner
Tsukuba J. Math. 32(1): 197-251 (June 2008). DOI: 10.21099/tkbjm/1496165198

Abstract

We determine periodic and aperiodic points of certain piecewise affine maps in the Euclidean plane. Using these maps, we prove for $\lambda \in \left\{ \frac{\pm 1 \pm \sqrt{5}}{2}, \pm \sqrt{2}, \pm{\sqrt{3}} \right \}$ that all integer sequences $(a_{k})_{k \in \mathbb{Z}}$ satisfying $0 \leq a_{k-1}+\lambda a_{k} + a_{k+1} \lt 1$ are periodic.

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Shigeki Akiyama. Horst Brunotte. Attila Pethö. Wolfgang Steiner. "Periodicity of Certain Piecewise Affine Planar Maps." Tsukuba J. Math. 32 (1) 197 - 251, June 2008. https://doi.org/10.21099/tkbjm/1496165198

Information

Published: June 2008
First available in Project Euclid: 30 May 2017

zbMATH: 1209.37018
MathSciNet: MR2433023
Digital Object Identifier: 10.21099/tkbjm/1496165198

Rights: Copyright © 2008 University of Tsukuba, Institute of Mathematics

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Vol.32 • No. 1 • June 2008
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