Heinz Hanßmann Hamiltonian Torus Bifurcations Related to Simple Singularities (166K, PostScript, gzipped and uuencoded) ABSTRACT. Lower dimensional $n$-tori in integrable and nearly integrable Hamiltonian systems with $n+1$ degrees of freedom are considered. The one-degree-of-freedom dynamics normal to the invariant tori is governed by (the singularities of) a family of planar Hamiltonian functions. The ensuing bifurcation scenarios are shown to survive both integrable and non-integrable perturbations.