A period formula for torus automorphisms
The paper determines the order of integer matrices \(A\in SL_2 (\mathbb{Z})\) on lattices \(L_N={1 \over N}\mathbb{Z}^2/ \mathbb{Z}^2\) of \(\mathbb{Q}^2/ \mathbb{Z}^2\), for \(N=P_n\equiv\) the number of \(n\)-periodic points (for the particular matrix-action on the rational 2-torus). The arguments lean heavily on arithmetical properties of (integer specializations of) certain Chebychev polynomials.
scientific article; zbMATH DE number 1941563