$\e_{kin}(u)$ and $\e_{kin}(c-h)$ correspond to the uniform and core-halo states in equilibrium.

![\[fig\_ec\] Plots of the relative values of (from top to the bottom) number of core particles $N'_{core}(\t)$, virial variable $\s'_{kin}(\t)$, and kinetic energy $\e'_{kin}(\t)$ for the system with $\e=-0.339$ and $N=250$.](fig11.eps){width=".45\textwidth"}

Figure \[fig\_ec\] indicates that during the initial stages of collapse the core grows faster than the kinetic energy and the virial variable. In addition, one can notice large reversible fluctuations in the number of core particles (the core grows up to 12% of its final value and then disappears) that are not matched by comparable scale fluctuations in the kinetic energy or virial variable. All these observations suggest that the density evolution causing the core formation plays the leading role in the process of collapse while the relaxation of kinetic energy follows. Once the collapse has started, the core grows to about a half of its final size in only $\d\t_{core}\sim 10^3$ for systems with $N=125$ – 500 particles, while the changes in kinetic energy during this interval of time are small. After this rapid initial stage the system relaxes more slowly, and finally after $\t_{coll}\sim 10^5$ reaches the equilibrium core-halo state. Our observations strongly suggest that 