PHASE-SPACE STRUCTURE OF A NEW INTEGRABLE SYSTEM RELATED TO HYDROGEN-ATOMS IN EXTERNAL FIELDS

We explore the detailed topological structure of the phase-space of th e recently discovered three-dimensional integrable but nonseparable Ha miltonian system with velocity dependent potential. Two three-paramete r families of three-dimensional tori which foliate the phase-space are identified. The complete classification, according to their topology, of the level sets corresponding to the critical points of the energy- momentum map, is accomplished. The relationship of the three-dimension al integrable system with important physical systems of current intere st, namely, the hydrogen atoms in circularly polarized (CP) fields, in crossed magnetic and electric fields and in crossed magnetic and CP f ields, is discussed.