It is shown that the cuspy density distributions observed in the cores of elliptical galaxies can be realized by dissipationless gravitational collapse .
The initial models consist of power-law density spheres such as \rho \propto r ^ { -1 } with anisotropic velocity dispersions .
Collapse simulations are carried out by integrating the collisionless Boltzmann equation directly , on the assumption of spherical symmetry .
From the results obtained , the extent of constant density cores , formed through violent relaxation , decreases as the velocity anisotropy increases radially , and practically disappears for extremely radially anisotropic models .
As a result , the relaxed density distributions become more cuspy with increasing radial velocity anisotropy .
It is thus concluded that the velocity anisotropy could be a key ingredient for the formation of density cusps in a dissipationless collapse picture .
The velocity dispersions increase with radius in the cores according to the nearly power-law density distributions .
The power-law index , n , of the density profiles , defined as \rho \propto r ^ { - n } , changes from n \approx 2.1 at intermediate radii , to a shallower power than n \approx 2.1 toward the centre .
This density bend can be explained from our postulated local phase-space constraint that the phase-space density accessible to the relaxed state is determined at each radius by the maximum phase-space density of the initial state .