  We associate with every locally expanding self-covering $f:M\to M$ of a
compact path connected metric space a finitely presented group $V_f$. We prove
that this group is a complete invariant of the dynamical system: two groups
$V_{f_1}$ and $V_{f_2}$ are isomorphic as abstract groups if and only if the
corresponding dynamical systems are topologically conjugate. We also show that
the commutator subgroup of $V_f$ is simple, and give a topological
interpretation of $V_f/V_f'$.
