Perturbed DF for stars located at the Sun’s position in the model, obtained with the analytical method described in Sect. 3. Left panel: velocity space (u, v). Right panel: perturbed DF in axisymmetric epicyclic action space (J_ϕ − J_circ, J_R), where J_circ is the angular momentum of a circular orbit at R = 8.2 kpc. The contours include (from darkest to lightest) 50, 68, 80, 90, and 95% of the stars. The radial velocity dispersion of the unperturbed DF f₀ at the Sun is σ_R = 45 km s⁻¹. The coloured lines correspond to each other in the two panels, and are plotted to identify the same features in velocity and action spaces. The green and yellow lines correspond to the corotation, the red line to the 2:1 (OLR) resonance for the m = 2 mode, the pink line to the 3:1 resonance of the m = 3 mode, the blue line to the 4:1 resonance of the m = 4 mode, and the purple line to the 6:1 resonance of the m = 6 mode.