The inverted pendulum: A singularity theory approach (Q1305487)

The authors study problems of parametrically forced Hamiltonian systems with an example of the inverted pendulum with small parametric forcing. The qualitative dynamics of the Poincaré map corresponding to the central periodic solution is studied via an approximating integrable normal form. The relation between the Poincaré map and its approximation is discussed in terms of perturbation theory. At bifurcation points local universal models are constructed in an appropriate symmetry context by using methods and techniques from the equivariant singularity theory.