Emmanuelle Julliard-Tosel

Astronomie et Systeme Dynamiques.
Bureau des longitudes.
Paris.
France.
julliard@bdl.fr
 

A non integrability result for the inverse square potential

Abstract: We show the analytical non-integrability of the $4$-body problem on the line for an inverse square potential and masses $(1,m,m,1),m\ne 1$. This is the first case left open by the integrability results of Jacobi ($3$bodies with arbitrary masses) and Calogero-Moser ($n$bodies with equal masses).