Recognition and classification for \(O(n)\)-equivariant bifurcations with \(O(n)\)-codimension less than 5 (Q1273099)

This article deals with the local bifurcation problem for the equation \[ g(x,\lambda)=0\;(g:\mathbb{R}^n\times \mathbb{R}\to\mathbb{R}^n) \] under the assumption that \[ g(\gamma x, \lambda)= \gamma g(x,\lambda)\;(\gamma\in \mathbb{O}(n), x\in\mathbb{R}^n, \lambda\in\mathbb{R}). \] The basic result is the complete description of the normal forms and universal unfolding for all 19 possible classes for the bifurcation phenomenon of the equation given above in the case \(\text{codim}_{O (n)}g\leq 4\). Moreover, for all 19 classes the corresponding recognizing conditions are presented.