  For a ${\mathbb Z}^{d}$-topological dynamical system $(X, T, {\mathbb
Z}^{d})$, an isomomorphism is a self-homeomorphism $\phi : X\to X$ such that
for some matrix $M\in {\rm GL}(d,{\mathbb Z})$ and any ${n}\in {\mathbb
Z}^{d}$, $\phi\circ T^{{n}}=T^{M{n}}\circ \phi$, where $T^{n}$ denote the
self-homeomorphism of $X$ given by the action of ${n}\in {\mathbb Z}^d$. The
collection of all the isomorphisms forms a group that is the normalizer of the
set of transformations $T^{n}$. In the one-dimensional case, isomorphisms
correspond to the notion of flip conjugacy of dynamical systems and by this
fact are also called reversing symmetries. These isomorphisms are not well
understood even for classical systems. We present a description of them for
odometers and more precisely for constant-base ${\mathbb Z}^{2}$-odometers,
which is surprisingly not simple. We deduce a complete description of the
isomorphisms of some minimal ${\mathbb Z}^{d}$-substitutive subshifts. This
enables us to provide the first example known of a minimal zero-entropy
subshift with the largest possible normalizer group.
