Year: 2008
Type: article
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.
Source: Tsukuba Journal of Mathematics
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1865617633