  Study of the dynamics of automorphisms of a group is usually focused on their
growth and/or finite orbits, including fixed points. In this paper, we
introduce properties of a different kind; using somewhat informal language, we
call them metric properties. Two principal characteristics of this kind are
called here the "curl" and the "flux"; there seems to be very little
correlation between these and the growth of an automorphism, which means they
are likely to be an essentially new tool for studying automorphisms. We also
observe that our definitions of the curl and flux are sufficiently general to
be applied to mappings of arbitrary metric spaces.
