ANGLE VARIABLES FOR NUMERICALLY FITTED ORBITAL TORI

Angle variables are constructed for orbital tori least-squares fitted to general potentials by the method of McGill & Binney. These angle variables enable one to determine the densities rho(j)(x) associated with the orbit that has given actions J. They also make it possible to treat any non-integrable potential as a perturbation on a nearby integrable one. As an illustration of this approach, Hamiltonian perturbation theory is used to derive the width of the 1:1 resonant-orbit family in a realistic model of the potential of a disc galaxy.