Generic Bifurcation of Hamiltonian Systems with Symmetry
Marsden, J. E.
appendix to Golubitsky and Stewart, Physica D, 24, (1987), 391-405
We study generic bifurcation of equilibria in one-parameter Hamiltonian systems with symmetry group
where eigenvalues of the linearized system go through zero. Theorem 3.3 classifies expected actions of
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.