M. Golubitsky and I.N. Stewart
Generic bifurcation of Hamiltonian systems with symmetry
Physica D. 24 (1987) 391-405.
We study generic bifurcations of equilibria in one-parameter Hamiltonian systems with symmetry group Gamma where eigenvalues of the linearized system go through zero. Theorem 3.3 classifies expected actions of Gamma on the generalized eigenspace of this zero eigenvalue. Generic one degree of freedom symmetric systems are classified in section 4; remarks concerning systems with more degrees of freedom are given in section 5.