  It 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.
