Angle variables for numerically fitted orbital tori

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Abstract
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 ⍴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 disk galaxy.

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