We investigate the dynamics of perturbation around inhomogeneous
stationary states of the Vlasov equation corresponding to the
Hamiltonian mean-field model.  The inhomogeneous background induces
a separatrix in the one-particle Hamiltonian system, and branch cuts
generically appear in the analytic continuation of the dispersion
relation in the complex frequency plane. We test the theory by
direct comparisons with N-body simulations, using two families of
distributions: inhomogeneous water-bags, and inhomogeneous thermal
equilibria.  In the water-bag case, which is not generic, no branch
cut appears in the dispersion relation, whereas in the thermal
equilibrium case, when looking for the root of the dispersion
relation closest to the real axis, we have to consider several
Riemann sheets. In both cases, we show that the roots of the
continued dispersion relation give useful, although not complete, 
information to understand the dynamics of a perturbation.

備考：  本研究は Julien Barre', Alain Olivetti (Univ. Nice, France)
	との共同研究である。