BIFURCATIONS IN A NONSYMMETRICAL CUBIC POTENTIAL

For a Hamiltonian corresponding to a perturbed couple of harmonic osci llators - but without symmetries - we obtain the evolution phase flow of the reduced Hamiltonian. The loss of symmetry produces a bifurcatio n that does not appear in the symmetric case, namely one where a stabl e point crosses an unstable point yielding a cusp in the level curve. This result may be considered as a warning to some of the conclusions derived in galactic dynamics from too symmetric Hamiltonian.