We perform a detailed comparison of the phase-space density traced by the
particle distribution in Gadget simulations to the result obtained with a
spherical Vlasov solver using the splitting algorithm. The systems considered
are apodized H\'enon spheres with two values of the virial ratio, R ~ 0.1 and
0.5. After checking that spherical symmetry is well preserved by the N-body
simulations, visual and quantitative comparisons are performed. In particular
we introduce new statistics, correlators and entropic estimators, based on the
likelihood of whether N-body simulations actually trace randomly the Vlasov
phase-space density. When taking into account the limits of both the N-body and
the Vlasov codes, namely collective effects due to the particle shot noise in
the first case and diffusion and possible nonlinear instabilities due to finite
resolution of the phase-space grid in the second case, we find a spectacular
agreement between both methods, even in regions of phase-space where nontrivial
physical instabilities develop. However, in the colder case, R=0.1, it was not
possible to prove actual numerical convergence of the N-body results after a
number of dynamical times, even with N=108 particles.Comment: 19 pages, 11 figures, MNRAS, in pres
