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arXiv · 1301.6621

Meromorphically integrable homogeneous potentials with multiple Darboux points

Thierry Combot
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Abstract

We prove that the only meromorphically integrable planar homogeneous potential of degree k <> -2,0,2 having a multiple Darboux point is the potential invariant by rotation. This case is a singular case of the Maciejewski-Przybylska relation on eigenvalues at Darboux points of homogeneous potentials, and needed before a case by case special analysis. The most striking application of this Theorem is the complete classification of integrable real analytic homogeneous potentials in the plane of negative degree.

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Thierry Combot. 2013-01-28. Meromorphically integrable homogeneous potentials with multiple Darboux points. https://arxiv.org/abs/1301.6621

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