Radial profiles at the shell-crossing using tenth-order LPT in the vicinity of (top panels) and (bottom panels). In the top panels, ϵ_2D is progressively varying in the range [0.9,1] with linear intervals of Δϵ = 0.1/64. In the bottom panels, ϵ_3D progressively changes from (0.97,0.97) to (1,1) with linear intervals of Δϵ = 0.03/64. From left to right, we present radial profiles of the normalised density , the velocity dispersion υ², the radial velocity dispersion the infall velocity –υ_r, and the pseudo phase-space density Q, respectively. In the lower inserts corresponding to logarithmic slopes, the horizontal dashed lines correspond to the values expected from singularity theory as computed in Appendix D and listed in Table 2.