Change in azimuthal angle for one radial period as a function of r. In general, Δφ depends on the energy and angular momentum of the particle. Here we replace the energy and angular momentum with their values averaged over radial bins of radius r. Halo c is shown with the dashed line, halo d is shown with the dotted line, and the semianalytic calculation for halo c is shown with the solid line. A value of ﹩\Delta \phi =\pi ﹩ (long‐dashed line) corresponds to a closed orbit where the particle makes two radial oscillations per orbit.