  The isoscalar octupole response of a heavy spherical nucleus is analyzed in a
semiclassical model based on the linearized Vlasov equation. The octupole
strength function is evaluated with different degrees of approximation. The
zero-order fixed-surface response displays a remarkable concentration of
strength in the $1\hbar\omega$ and $3\hbar\omega$ regions, in excellent
agreement with the quantum single-particle response. The collective
fixed-surface response reproduces both the high- and low-energy octupole
rsonances, but not the low-lying $3^{-}$ collective states, while the
moving-surface response function gives a good qualitative description of all
the main features of the octupole response in heavy nuclei. The role of
triangular nucleon orbits, that have been related to a possible instability of
the spherical shape with respect to octupole-type deformations, is discussed
within this model. It is found that, rather than creating instability, the
triangular trajectories are the only classical orbits contributing to the
damping of low-energy octupole excitations.
