INTEGRABLE PLANAR HOMOGENEOUS POTENTIALS OF DEGREE-1 WITH SMALL EIGENVALUES
| Affiliation auteurs | Affiliation ok |
| Titre | INTEGRABLE PLANAR HOMOGENEOUS POTENTIALS OF DEGREE-1 WITH SMALL EIGENVALUES |
| Type de publication | Journal Article |
| Year of Publication | 2016 |
| Auteurs | Combot T |
| Journal | ANNALES DE L INSTITUT FOURIER |
| Volume | 66 |
| Pagination | 2253-2298 |
| Type of Article | Article |
| ISSN | 0373-0956 |
| Mots-clés | D-finiteness, higher variational equations, Homogeneous potentials, Morales-Ramis theory |
| Résumé | We give a complete classification of meromorphically integrable homogeneous potentials V of degree -1 which are real analytic on R-2 \textbackslash {0}. In the more general case when V is only meromorphic on an open set of an algebraic variety, we give a classification of all integrable potentials having a Darboux point c with V' (c) = -c, c(1)(2)+ c(2)(2) not equal 0 and Sp(del V-2(c)) subset of {-1, 0, 2}. We eventually present a conjecture for the other eigenvalues and the degenerate Darboux point case V' (c) = 0. |