Bifurcations in Hamiltonian Systems with Symmetry

The goal of this lecture is to outline some recent work of the lecturer, M. Golubitsky, I. Stewart, E. Knobloch, A. Mahalov and T. Ratiu on bifurcations in Hamiltonian systems with symmetry. We will survey some earlier work with D. Lewis, T. Ratiu and others to set the stage for the problems to be discussed. Many of the basic results in bifurcation of mechanical systems is available in, for example, Marsden [1992] and Duistermaat [1983] and references therein.