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Extended system, bifurcation problem and high order singularities. (English) Zbl 0829.65076
Authors’ abstract: We consider two extended systems. When using them for the two parameter bifurcation problems, the simple bifurcation point with regard to $$\lambda$$ can turn into the simple turning point with regard to $$\mu$$. Simple high order bifurcation points are first studied without using the symmetry condition.
##### MSC:
 65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx) 47J25 Iterative procedures involving nonlinear operators 58E07 Variational problems in abstract bifurcation theory in infinite-dimensional spaces