Periodic Perturbations of Codimension-Two Bifurcations with a Double
Zero Eigenvalue in Two-Dimensional Dynamical Systems with Symmetry

We study bifurcation behavior in periodic perturbations of
two-dimensional symmetric systems exhibiting codimension-two
bifurcations with a double eigenvalue. We are interested in the case
in which the frequency is sufficiently small. We transform the
periodically perturbed system to a simpler one which is a periodic
perturbation of the normal form for codimension-two bifurcations with
a double zero eigenvalue and symmetry, and apply the subharmonic and
homoclinic Melnikov methods to analyze bifurcations occurring in the
system. Especially, we show that there exist transverse homoclinic or
heteroclinic orbits, which yield chaotic dynamics, in wide parameter
regions.