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 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 .