Periodicity of certain piecewise affine planar maps
Résumé
We determine periodic and aperiodic points of certain piecewise affine maps in the Euclidean plane. Using these maps, we prove that all integer sequences $(a_k)_{k\in\mathbb Z}$ satisfying $0\le a_{k-1}+\lambda a_k +a_{k+1}<1$ for some (fixed) $\lambda \in \{\frac{\pm1\pm\sqrt{5}}{2},\pm\sqrt{2}\}$ are periodic.
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