  A semiclassical theory of linear response in finite Fermi systems, based on
the Vlasov equation, and its applications to the study of isoscalar vibrations
in heavy nuclei are reviewed. It is argued that the Vlasov equation can be used
to study the response of small quantum systems like (heavy) nuclei in regimes
for which the finite size of the system is more important than the collisions
between constituents. This requires solving the linearized Vlasov equation for
finite systems, however, in this case the problem of choosing appropriate
boundary conditions for the fluctuations of the phase-space-density is
non-trivial. Calculations of the isoscalar response functions performed by
using different boundary conditions, corresponding to fixed and moving nuclear
surface, are compared for different multipoles and it is found that, in a
sharp-surface model, the moving-surface boundary conditions give better
agreement with experiment. The semiclassical strength functions given by this
theory are strikingly similar to the results of analogous quantum calculations,
in spite of the fact that shell effects are not included in the theory, this
happens because of a well known close relation between classical trajectories
and shell structure.
