Periodicity of certain piecewise affine planar maps

We determine periodic and aperiodic points of certain piecewise affine maps in the Euclidean plane. Using these maps, we prove for λ ∈ { ±1± √ 5 2 , ± √ 2, ± √ 3} that all integer sequences (ak)k∈Z satisfying 0 ≤ ak−1 + λak + ak+1 < 1 are periodic.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Shigeki Akiyama, Horst Brunotte, Attila Pethö, Wolfgang Steiner
• Keywords: Aperiodic Points, Certain Piecewise Affine, CORR 2007, Education, Euclidean Plane