An algebraic geometric method to calculate branches near a bifurcation point
Although not explicitly stated in the introduction, the paper deals only with systems of polynomial equations \(F(x)=0,\quad F: {\mathbb{R}}^{n+1}\to {\mathbb{R}}^ n.\) In particular, the problem is studied how to calculate solution branches near a bifurcation point. The algebraic geometric concept of ``blowing up'' is utilized to regularize the Jacobian at the bifurcation point. Then the different branches are calculated by a standard continuation method. The original branches are obtained by ``blowing them down''. The method is illustrated for a simple example.
scientific article; zbMATH DE number 4159981
scientific article