  The topological analysis from Bjorkman (1995) for the standard model that
describes the winds from hot stars by Castor, Abbott & Klein (1975) has been
extended to include the effect of stellar rotation and changes in the
ionization of the wind. The differential equation for the momentum of the wind
is non--linear and transcendental for the velocity gradient. Due to this
non--linearity the number of solutions that this equation possess is not known.
After a change of variables and the introduction of a new physically
meaningless independent variable, we manage to replace the non--linear momentum
differential equation by a system of differential equations where all the
derivatives are {\it{explicitely}} given. We then use this system of equations
to study the topology of the rotating--CAK model. For the particular case when
the wind is frozen in ionization ($\delta=0$) only one physical solution is
found, the standard CAK solution, with a X--type singular point. For the more
general case ($\delta \neq 0$), besides the standard CAK singular point, we
find a second singular point which is focal--type (or attractor). We find also,
that the wind does not adopt the maximal mass--loss rate but almost the
minimal.
