EQUIVARIANT SINGULARITY THEORY WITH DISTINGUISHED PARAMETERS - 2 CASE-STUDIES OF RESONANT HAMILTONIAN-SYSTEMS

We consider Hamiltonian systems near equilibrium that can be (formally ) reduced to one degree of freedom. Spatiotemporal symmetries play a k ey role. The planar reduction is studied by equivariant singularity th eory with distinguished parameters. The method is illustrated on the c onservative spring-pendulum system near resonance, where it leads to i ntegrable approximations of the iso-energetic Poincare map. The novelt y of our approach is that we obtain information on the whole dynamics, regarding the (quasi-) periodic solutions, the global configuration o f their invariant manifolds, and bifurcations of these.