  Paper in honour of Freeman Dyson on the occasion of his 80th birthday.
  Normal N-body systems relax to equilibrium distributions in which classical
kinetic energy components are 1/2 kT, but, when inter-particle forces are an
inverse cubic repulsion together with a linear (simple harmonic) attraction,
the system pulsates for ever. In spite of this pulsation in scale, r(t), other
degrees of freedom relax to an ever-changing Maxwellian distribution. With a
new time, tau, defined so that r^2d/dt =d/d tau it is shown that the remaining
degrees of freedom evolve with an unchanging reduced Hamiltonian. The
distribution predicted by equilibrium statistical mechanics applied to the
reduced Hamiltonian is an ever-pulsating Maxwellian in which the temperature
pulsates like r^-2. Numerical simulation with 1000 particles demonstrate a
rapid relaxation to this pulsating equilibrium.
