Two parameter families of binary differential equations
The author studies the topological classification of singularities of local codimension \(2\) of binary differential equations of the form \(ady^2+2bdxdy+cdx^2=0\) with smooth coefficients \(a\), \(b\), \(c\) in the case that all coefficients vanish at the singularity. The topological models are obtained by an extension of Guíñez' blowing up technique. It is shown that three different classes exist and for each class a local normal form of the singularity itself and of the corresponding generic two-parameter family arising in bifurcation.
scientific article; zbMATH DE number 5362918