  We propose an analytical method to describe a matter density profile near a
galaxy center. The description is based on the study of the distribution
function of particles over possible trajectories. We establish a relation
between the central slope of density profile and the near-origin behavior of
the angular momentum distribution function. We consider both a spherically
symmetric (on average) matter distribution as well as deviations from it. If
the density profile forms in a background of spherical gravitation potential
then a core-type distribution arises. A regular matter may behave in such way
if the background potential was formed by the dark matter. In the presence of
deviation from spherical symmetry the formation of cusp-type distribution is
possible. Moreover, a reduction of spherical symmetry to the axial one leads to
a less steep cusp profile. The complete symmetry breaking (which corresponds,
in particular, to the common setup of numerical simulations), leads to a
steeper cusp profile.
