CLASSIFICATION AND UNFOLDINGS OF 1 2-RESONANT HOPF-BIFURCATION/

In this paper, we study the bifurcations of periodic solutions from an equilibrium point of a differential equation whose linearization has two pairs of simple pure imaginary complex conjugate eigenvalues which are in 1:2 ratio. This corresponds to a Hopf-Hopf mode interaction wi th 1:2 resonance, as occurs in the context of dissipative mechanical s ystems. Using an approach based on Liapunov-Schmidt reduction and sing ularity theory, we give a framework in which to study these problems a nd their perturbations in two cases: no distinguished parameter, and o ne distinguished (bifurcation) parameter. We give a complete classific ation of the generic cases and their unfoldings.