  The dynamical excitation of asteroids due to mean motion resonant
interactions with planets is enhanced when their parent star leaves the main
sequence. However, numerical investigation of resonant outcomes within
post-main-sequence simulations is computationally expensive, limiting the
extent to which detailed resonant analyses have been performed. Here, we
combine the use of a high-performance computer cluster and the general
semianalytical libration width formulation of Gallardo et al. (2021) in order
to quantify resonant stability, strength and variation instigated by stellar
evolution for a single-planet system containing asteroids on both crossing and
non-crossing orbits. We find that resonant instability can be accurately bound
with only main-sequence values by computing a maximum libration width as a
function of asteroid longitude of pericentre. We also quantify the relative
efficiency of mean motion resonances of different orders to stabilize versus
destabilize asteroid orbits during both the giant branch and white dwarf
phases. The 4:1, 3:1 and 2:1 resonances represent efficient polluters of white
dwarfs, and even when in the orbit-crossing regime, both the 4:3 and 3:2
resonances can retain small reservoirs of asteroids in stable orbits throughout
giant branch and white dwarf evolution. This investigation represents a
preliminary step in characterising how simplified extrasolar Kirkwood gap
structures evolve beyond the main-sequence.
