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arXiv · 0704.3674

Periodicity of certain piecewise affine planar maps

Shigeki Akiyama·Horst Brunotte·Attila Petho·Wolfgang Steiner
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Abstract

We determine periodic and aperiodic points of certain piecewise affine maps in the Euclidean plane. Using these maps, we prove for $λ\in\{\frac{\pm1\pm\sqrt5}2,\pm\sqrt2,\pm\sqrt3\}$ that all integer sequences $(a_k)_{k\in\mathbb Z}$ satisfying $0\le a_{k-1}+λa_k+a_{k+1}<1$ are periodic.

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Shigeki Akiyama, Horst Brunotte, Attila Petho, Wolfgang Steiner. 2008-09-16. Periodicity of certain piecewise affine planar maps. https://arxiv.org/abs/0704.3674

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