Classification of pitchfork bifurcations and their computation (Q1825602)

Pitchfork bifurcation points of degree \(n\geq 3\) (i.e., with normal form \(x^ n\pm \lambda x)\) are shown to be regular roots of defining equations \((=\) extended system). The implementation of one Newton iteration is proposed in the case \(n=3\). It costs the solution of 16 auxiliary linear systems with the same matrix (a regularized differential of the original mapping).