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arXiv · 1402.7249

Canonical methods of constructing invariant tori by phase-space sampling

Teemu Laakso·Mikko Kaasalainen
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Abstract

Invariant tori in phase space can be constructed via a nonperturbative canonical transformation applied to a known integrable Hamiltonian H. Hitherto, this process has been carried through with H 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 H can be based on a St\"ackel 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.

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Teemu Laakso, Mikko Kaasalainen. 2014-02-28. Canonical methods of constructing invariant tori by phase-space sampling. https://doi.org/10.1016/j.physd.2012.09.010

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