Generic one-parameter versal unfoldings of deformations of symmetric Hamiltonian systems in 1:1 resonance

We consider Hamiltonian systems in 1:1 resonance in the presence of symmetry. We give some new proofs for known results concerning the classification of generic one-parameter deformations of equivariant linear systems and the passing and splitting of eigenvalues. We show that for nonlinear systems in two degrees of freedom the bifurcation of periodic solutions in the generic passing cases can be linearized. We conclude with several examples.