A point (x*, *, *) is called a winged cusp point of the nonlinear system F (x, , ) = 0 , F : n × 1 × 3 n, if
and if the Ljapunov-Schmidt reduced function has the normal form g(, ) = ±3 ± 2, g : 1 × 1 1. A minimally extended system F (x, , ) = 0, f(x, , ) = 0 is proposed for defining winged cusp points, where f : n × 1 × 3 4 are 4 scalar functions characterizing the winged cusp. The functions fi : n × 1 × 3 1, i = 1, ..., 4, depend on the partial derivatives g, g, 2g, and g. For the description of the fi an evaluable type of Ljapunov-Schmidt reduced function is introduced. The regular solution (x*, *, *) of the (n + 4)-dimensional extended system delivers the desired winged cusp point (x*, *) as first part. For numerically solving these systems, a two-stage Newton-type method are proposed. Computational differentiation is applied for computing the several partial derivatives needed. A numerical example is given.
The talk is based on the papers:
 Schnabel, U., Pönisch, G., Janovský, V. Reduced functions characterizing singular points and their relations. Preprint IOKOMO–04–1999, TU Dresden, 1999.
 Schnabel, U., Walther, A. Berechnung singulärer Punkte: Newtonverfahren und Automatische Differentiation. Preprint IOKOMO–05–1999, TU Dresden, 1999.