6533b7ddfe1ef96bd12735e0
RESEARCH PRODUCT
Integrability and Non Integrability of Some n Body Problems
Thierry Combotsubject
[ MATH ] Mathematics [math]Pure mathematicsDegree (graph theory)Integrable systemCentral configurationsn-body problem[ PHYS.ASTR ] Physics [physics]/Astrophysics [astro-ph]010102 general mathematicsMathematical analysisDifferential Galois theory01 natural sciences010101 applied mathematicsDifferential Galois theoryHomogeneousSimple (abstract algebra)Integrable systems0101 mathematicsInvariant (mathematics)[MATH]Mathematics [math]Homogeneous potentialMorales-Ramis theory[PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph]MathematicsVector spacedescription
International audience; We prove the non integrability of the colinear 3 and 4 body problem, for any positive masses. To deal with resistant cases, we present strong integrability criterions for 3 dimensional homogeneous potentials of degree −1, and prove that such cases cannot appear in the 4 body problem. Following the same strategy, we present a simple proof of non integrability for the planar n body problem. Eventually, we present some integrable cases of the n body problem restricted to some invariant vector spaces.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-01-01 |