Uniform trace formulae for SU(2) and SO(3) symmetry breaking

We develop uniform approximations for the trace formula for non-integrable systems in which SU(2) symmetry is broken by a non-linear term of the Hamiltonian. As specific examples, we investigate H'enon-Heiles type potentials. Our formalism can also be applied to the breaking of SO(3) symmetry in a three-dimensional cavity with axially-symmetric quadrupole deformation.