Canonical methods of constructing invariant tori by phase–space sampling

Invariant tori in phase space can be constructed via a nonperturbative canonical transformation applied to a known integrable Hamiltonian HH. Hitherto, this process has been carried through with HH corresponding to the isochrone potential and the harmonic oscillator. In this paper, we expand the applicability regime of the torus construction method by demonstrating that HH can be based on a Stäckel potential, the most general known form of an integrable potential. Also, we present a simple scheme, based on phase space sampling, for recovering the angle variables on the constructed torus. Numerical examples involving axisymmetric galactic potentials are given.

► Construction of invariant phase–space tori for an arbitrary Hamiltonian.
► The method is canonical and based on ellipsoidal Stäckel potentials.
► Straightforward algorithm for obtaining the angle variables.