Managing resonant trapped orbits in our Galaxy
  Galaxy modelling is greatly simplified by assuming the existence of a global
system of angle-action coordinates. Unfortunately, global angle-action
coordinates do not exist because some orbits become trapped by resonances,
especially where the radial and vertical frequencies coincide. We show that in
a realistic Galactic potential such trapping occurs only on thick-disc and halo
orbits (speed relative to the guiding centre >~80 km/s). We explain how the
Torus Mapper code (TM) behaves in regions of phase space in which orbits are
resonantly trapped, and we extend TM so trapped orbits can be manipulated as
easily as untrapped ones. The impact that the resonance has on the structure of
velocity space depends on the weights assigned to trapped orbits. The impact is
everywhere small if each trapped orbit is assigned the phase space density
equal to the time average along the orbit of the DF for untrapped orbits. The
impact could be significant with a different assignment of weights to trapped
orbits.
