It is a very degenerate situation in Hopf bifurcation theory that all (bifurcating) periodic solutions occur for the parameter value of the bifurcation point. In principle such a singularity has infinite codimension. Therefore the problem of classification and equivalence of such bifurcation problems is very difficult. The author solves precisely this problem. He motivates his studies by pointing out it can be generic for certain classes of dynamical systems (for example Hamiltonian systems).