2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69873It is known that for $n \geq 3$ centres and positive energies the $n$-centre problem of celestial mechanics leads to a flow with a strange repellor and positive topological entropy. Here we consider the energies above some threshold and show: Whereas for arbitrary $g >1$ independent integrals of Gevrey class $g$ exist, no real-analytic (that is, Gevrey class 1) independent integral exists.22 pages, a short announcement see in math.DS/0312429Dynamical SystemsMathematical Physicstext