  The Pontryagin dual of the twisted Alexander module for a d-component link
and GL(N,Z) representation is an algebraic dynamical system with an elementary
description in terms of colorings of a diagram. In the case of a knot, its
associated topological entropy is the logarithmic growth rate of the number of
torsion elements in the twisted first-homology group of r-fold cyclic covers of
the knot complement, as r goes to infinity.
  Total twisted representations are introduced, and their properties are
studied. The twisted Alexander polynomial obtained from any nonabelian
parabolic SL(2,C) representation of a 2-bridge knot group is seen to be
nontrivial. The zeros of any twisted Alexander polynomial of a torus knot
corresponding to a parabolic SL(2,C) representation or a finite-image
permutation representation are shown to be roots of unity.
