  We consider the behavior of spherically symmetric Einasto halos composed of
gravitating particles in the Fokker-Planck approximation. This approach allows
us to consider the undesirable influence of close encounters in the N-body
simulations more adequately than the generally accepted criteria. The Einasto
profile with index $n \approx 6$ is a stationary solution of the Fokker-Planck
equation in the halo center. There are some reasons to believe that the
solution is an attractor. Then the Fokker-Planck diffusion tends to transform a
density profile to the equilibrium one with the Einasto index $n \approx 6$. We
suggest this effect as a possible reason why the Einasto index $n \approx 6$
occurs so frequently in the interpretation of N-body simulation results. The
results obtained cast doubt on generally accepted criteria of N-body simulation
convergence.
