|XXVIII Workshop on Geometric Methods in Physics||28.06-04.07.2009|
Classical and quantum fold catastrophe in the presence of axial symmetry
We introduce a family of Hamiltonians with two degrees of freedom, axial symmetry and complete integrability. The potential function depends on coordinates and one control parameter. A fold catastrophe typically occurs in such a family of potentials and its consequences on the global dynamics are investigated through the energy-momentum map which defines the singular fibration of the four-dimensional phase space. Both classical and quantum mechanical points of view will be presented.