(untitled) (Journal of Computational Mathematics, 1996)
In the paper we are concerned with double S-breaking cubic turning points of two-parameter nonlinear problems in the presence of Z_2-symmetry. Three extended systems are proposed to determine double S-breaking cubic turning points. We show that there exist two kinds of singular point path passing through double S-breaking cubic turning point. One is the simple quadratic turning point path, the other is the pitchfork bifurcation point path.