  Intermittent dynamics is characterized by long periods of different types of
dynamical characteristics, for instance almost periodic dynamics alternated by
chaotic dynamics. Critical intermittency is intermittent dynamics that can
occur in iterated function systems, and involves a superattracting periodic
orbit.
  This paper will provide and study examples of iterated function systems by
two rational maps on the Riemann sphere that give rise to critical
intermittency. The main ingredient for this is a superattracting fixed point
for one map that is mapped onto a common repelling fixed point by the other
map. We include a study of topological properties such as topological
transitivity.
