Canonical methods of constructing invariant tori by phase-space sampling
Mathematical Physics
2014-03-04 v1 math.MP
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.
Cite
@article{arxiv.1402.7249,
title = {Canonical methods of constructing invariant tori by phase-space sampling},
author = {Teemu Laakso and Mikko Kaasalainen},
journal= {arXiv preprint arXiv:1402.7249},
year = {2014}
}