Hyperbolic toral automorphism
= Hyperbolic toral automorphism
{title2=$x\mapsto Ax\pmod{\mathbb Z^n}$}
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 $\begin{pmatrix}2&1\\1&1\end{pmatrix}$ has eigenvalues $(3\pm\sqrt5)/2$, yielding one contracting and one expanding direction.