Bifurcations of continuous dynamical systems under extreme and new transversality conditions
The paper considers the local structure of the zero set \(f(\mu,x)=0\), where \(\mu\) is a parameter, under the assumption that \(f:\mathbb{R}^2\rightarrow \mathbb{R}\) is analytic, near a bifurcation point. Results characterizing the nature of the bifurcation (transcritical, pitchfork) are derived for degenerate cases, for which the transversality conditions required by the classical bifurcation theorems do not hold.
scientific article; zbMATH DE number 5550271
scientific article