  In this paper we demonstrate the generation of gravitational caustics that
appear due to the geodesic focusing in a self-gravitating N-body system. The
gravitational caustics are space regions where the density of particles is
higher than the average density in the surrounding space. It is suggested that
the intrinsic mechanism of caustics generation is responsible for the formation
of the cosmological Large Scale Structure that consists of matter
concentrations in the form of galaxies, galactic clusters, filaments, and vast
regions devoid of galaxies.
  In our approach the dynamics of a self-gravitating N-body system is
formulated in terms of a geodesic flow on a curved Riemannian manifold of
dimension 3N equipped by the Maupertuis's metric. We investigate the sign of
the sectional curvatures that defines the stability of geodesic trajectories in
different parts of the phase space. The regions of negative sectional
curvatures are responsible for the exponential instability of geodesic
trajectories, deterministic chaos and relaxation phenomena of globular clusters
and galaxies, while the regions of positive sectional curvatures are
responsible for the gravitational geodesic focusing and generation of caustics.
By solving the Jacobi and the Raychaudhuri equations we estimated the
characteristic time scale of generation of gravitational caustics, calculated
the density contrast on the caustics and compared it with the density contrasts
generated by the Jeans-Bonnor-Lifshitz-Khalatnikov gravitational instability
and that of the spherical top-hat model of Gunn and Gott.
