Meromorphically integrable homogeneous potentials with multiple Darboux points
Dynamical Systems
2013-01-29 v1 Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.1301.6621,
title = {Meromorphically integrable homogeneous potentials with multiple Darboux points},
author = {Thierry Combot},
journal= {arXiv preprint arXiv:1301.6621},
year = {2013}
}
Comments
22 pages