Vertical action and its evolution. Left and middle columns: 2D maps of the vertical action J_z plotted in different coordinates, (L_z, J_R′=J_R − θ(−L_z)L_z) (first column), (L_z, ω_z/κ) (second column), and (2(Ω − Ω_p)/κ, ω_z/κ) (third column). Top row: Average value of the action in the pixel. Bottom row: Mean changes in J_z from t = 300 to t = 400 (actions and frequencies refer to the moment t = 400). The vector fields in the bottom rows demonstrate the average flow of orbits in given planes over five time units (from 400 to 405). The thin gray lines in each plot represent isodensity contours. The thick gray lines in the top left plot correspond to the lines with the same value of the adiabatic invariant J_v = J_R′+J_z + L_z/2. The vertical green lines in the middle column indicate the location of the CR and ILR. Right column: Snapshots (xy and xz) of the bar orbits (abnormal orbits; see Zozulia et al. 2024) at t = 400 with different frequency ratios ω_z/κ > 1 (top two plots) and ω_z/κ < 1 (bottom two plots).