The Inverted Pendulum: A Singularity Theory Approach

The inverted pendulum with small parametric forcing is considered as an example of a wider class of parametrically forced Hamiltonian systems. The qualitative dynamics of the Poincaré map corresponding to the central periodic solution is studied via an approximating integrable normal form. At bifurcation points we construct local universal models in the appropriate symmetry context, using equivariant singularity theory. In this context, structural stability can be proved under generic conditions.