At a planar saddle equilibrium with , positive saddle quantity is equivalent to saddle index . The local passage followed by the regular return has leading transverse map , . Its derivative diverges as , so a nearby periodic orbit created by the saddle-loop splitting is repelling. This local mechanism agrees with the growth of the unstable periodic orbit born at a subcritical Hopf bifurcation in the quadratic Bogdanov–Takens unfolding.