TORUS CONSTRUCTION IN POTENTIALS SUPPORTING DIFFERENT ORBIT FAMILIES

The scheme introduced by McGill & Binney and Binney & Kumar (Papers I and II), for the construction of phase-space tori that are approximate invariant tori of a given Hamiltonian, is extended and refined. Where as Papers I and II concentrated on orbits in the meridional planes of axisymmetric potentials, here tori are constructed for box and loop or bits in planar, barred potentials. We demonstrate the applicability of the scheme to potentials that have two major orbit families rather th an the single family of the meridional-plane problem. We refine the me thods of Papers I and II in two respects: (i) by combining the generat ing function approach of Paper I with point transformations, we are ab le to map toy tori into target tori that are not otherwise accessible; (ii) we introduce a scheme for the recovery of angle variables that i s superior to that introduced in Paper II. We illustrate the method by applying it both to Stackel potentials and to potentials that are not separable and in which not all orbits belong to the two major orbit f amilies of Stackel potentials.