  We use analytical and numerical methods to investigate the equations for
cohomogeneity one shrinking gradient Ricci solitons. We show the existence of a
winding number for this system around the subvariety of phase space
corresponding to Einstein solutions and obtain some estimates for it. We prove
a non-existence result for certain orbit types, analogous to that of Bohm in
the Einstein case. We also carry out numerical investigations for selected
orbit types.
