Cat map (source code)
= Cat map
{title2=$(x,y)\longmapsto(2x+y,x+y)\pmod1$}
The <cat map> is the <area-preserving map>[area-preserving] <toral automorphism> induced by the <integer matrix> $A=\begin{pmatrix}2&1\\1&1\end{pmatrix}$. Its <eigenvalues> are $(3\pm\sqrt5)/2$, giving one expanding and one contracting <eigenvector>[eigendirection]. Cutting its image <parallelogram> by the <integer> grid and translating the pieces <modular arithmetic>[modulo one] gives a concrete geometric construction on the <square>[unit square].
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