Hyperbolic toral automorphism ($x\mapsto Ax(\mathrm{mod}{\mathbb{Z}}^n)$)

An integer invertible matrix with no eigenvalue on the unit circle induces a hyperbolic toral automorphism. Its stable and unstable tangent subspaces are the corresponding generalized eigenspaces. The matrix $\left(\begin{array}{cc}2& 1\\ 1& 1\end{array}\right)$ has eigenvalues $(3\pm \sqrt{5})/2$, yielding one contracting and one expanding direction.