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Article Dans Une Revue Nonlinear Dynamics Année : 2021

Integrability of the generalised Hill problem

Résumé

We consider a certain two-parameter generalisation of the planar Hill lunar problem. We prove that for nonzero values of these parameters the system is not integrable in the Liouville sense. For special choices of parameters the system coincides with the classical Hill system, the integrable synodical Kepler problem or the integrable parametric Hénon system. We prove that the synodical Kepler problem is not super-integrable, and that the parametric Hénon problem is super-integrable for infinitely many values of the parameter.

Dates et versions

hal-03509794 , version 1 (04-01-2022)

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Thierry Combot, Andrzej Maciejewski, Maria Przybylska. Integrability of the generalised Hill problem. Nonlinear Dynamics, 2021, ⟨10.1007/s11071-021-07040-8⟩. ⟨hal-03509794⟩
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