Abstract
If the undisturbed Hamiltonian F0 is a function of the momenta only, then a variant of the Hori-Lie series perturbation method achieves a solution to any order with a single canonical transformation, without the use of the pseudo-time.
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References
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Cui, DX., Garfinkel, B. A variant of the Hori-Lie series method. Celestial Mechanics 35, 89–94 (1985). https://doi.org/10.1007/BF01229114
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DOI: https://doi.org/10.1007/BF01229114