M. Golubitsky and I. Stewart
Generic Bifurcation of Hamiltonian Systems with Symmetry
Physica 24D (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.