Vertical action and its evolution for captured orbits. Left and middle columns: 2D density maps (bar and disk) in the background and 2D maps (superimposed in the foreground) of J_z for orbits that were flat (J_z < 0.05) at t = 300 and trapped into the bar over the time interval of t = 300 − 400. Different time moments are shown from top to bottom, t = 300 (top row), 400 (middle row), and 500 (bottom row). The thin gray lines in each plot represent the isodensity contours of trapped orbits. In the left column, the thick gray lines correspond to isolines of the same value of the adiabatic invariant J_v = J_R′+J_z + L_z/2, and the thick cyan line corresponds to the frequency ratio isoline ω_z/κ = 1. The vertical blue lines in the middle column indicate the location of the CR and ILR. Right column: Snapshots (xy and xz) of the trapped orbits at the corresponding time moments.