  We investigate dynamical properties of the set of permutations of
$\mathbb{Z}^d$ with restricted movement, i.e., permutations $\pi $ of
$\mathbb{Z}^d$ such that $\pi (\mathbf{n})-\mathbf{n}$ lies, for every
$\mathbf{n}\in \mathbb{Z}^d$, in a prescribed finite set $A\subset
\mathbb{Z}^d$. For $d=1$, such permutations occur, for example, in restricted
orbit equivalence, or in the calculation of determinants of certain bi-infinite
multi-diagonal matrices. For $d\ge2$ these sets of permutations provide natural
classes of examples of multidimensional shifts of finite type.
