  Dynamical friction is often modeled with reasonable accuracy by the widely
used Chandrasekhar formula. However, in some circumstances, Chandrasekhar's
local and uniform approximations can break down severely. An astrophysically
important example is the "core stalling" phenomenon seen in N-body simulations
of massive perturber inspiralling into the near-harmonic potential of a stellar
system's constant-density core (and possibly also in direct observations of
dwarf galaxies with globular clusters). In this paper we use the linearized
collisionless Boltzmann equation to calculate the global response of a cored
galaxy to the presence of a massive perturber. We evaluate the density
deformation, or wake, due to the perturber and study its geometrical structure
to better understand the phenomenon of core stalling. We also evaluate the
dynamical friction torque acting on perturber from the Lynden-Bell--Kalnajs
(LBK) formula. In agreement with past work, we find that the dynamical friction
force arising from corotating resonances is greatly weakened, relative to the
Chandrasekhar formula, inside a constant density core. In contrast to past
work, however, we find that a population of previously neglected high-order and
non-corotating resonances sustain a minimum level of frictional torque at ~10 %
of the torque from Chandrasekhar formula. This suggests that complete core
stalling likely requires phenomena beyond the LBK approach; we discuss several
possible explanations. Additionally, to study core stalling for multiple
perturbers, we investigate approximate secular dynamical interactions (akin to
Lidov-Kozai dynamics) between two perturbers orbiting a cored stellar system
and derive a criterion for instability arising due to their close encounters.
