Destruction of the horseshoe orbits near the CR in the vicinity of an ILR or OLR of a secondary wave. First column: the red/green particles initially start on rings just inside/outside the CR (dashed black circle) of an m = 2 spiral wave. The top and bottom plots are identical. Second column: same initial conditions, but near the 4:1 OLR (top) or 4:1 ILR (bottom) of an m = 4 wave. Third column: same initial conditions, but particles are perturbed by both spiral waves. Note that a secondary wave of only 1/3 the strength of the first one is enough to disrupt the horseshoe orbits near the CR. Simulations from Minchev & Quillen (2006).