Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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
$\lambda\in\{\frac{\pm1\pm\sqrt5}2,\pm\sqrt2,\pm\sqrt3\}$ 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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The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics