Periodicity of certain piecewise affine planar maps

Details Periodicity of certain piecewise affine planar maps Periodicity of certain piecewise affine planar maps

2007-04-27

arxiv.org/abs/0704.3674v3

Tsukuba Journal of Mathematics 32, 1 (2008) 197-251

Mathematics

Dynamical Systems

Scientific paper

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

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