Homography
Periodic homographies

The homography h = (1 1 0 1) {\displaystyle h={\begin{pmatrix}1&1\\0&1\end{pmatrix}}} is periodic when the ring is Z / n Z (the integers modulo n) since then h n = (1 n 0 1) = (1 0 0 1). {\displaystyle h^{n}={\begin{pmatrix}1&n\\0&1\end{pmatrix}}={\begin{pmatrix}1&0\\0&1\end{pmatrix}}.} Arthur Cayley was interested in periodicity when he calculated iterates in 1879. In his review of a brute force approach to periodicity of homographies, H. S. M. Coxeter gave this analysis:
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