  We study the Weyl chamber length boundary both of the Hitchin and of the
maximal character varieties and determine therein an open set of discontinuity
for the action of the mapping class group. This result is obtained as
consequence of a canonical decomposition of a geodesic current on a surface of
finite type arising from a topological decomposition of the surface along
special geodesics. We show that each component either is associated to a
measured lamination or has positive systole. For a current with positive
systole, we show that the intersection function on the set of closed curves is
bi-Lipschitz equivalent to the length function with respect to a hyperbolic
metric.
  The results of this paper on currents generalise the ones in
arXiv:1710.07060v1 to the case of surfaces of finite area with geodesic
boundary. Concerning the Weyl chamber boundary we improve on the results in
arXiv:1710.07060v1 by showing that for higher rank groups, said open set of
discontinuity is not empty. We give also explicit examples in the case of the
$SL(3,\mathbb R)$-Hitchin component.
