Determinism of genesis of large-scale structures in astrophysics

The criteria for the formation of non-stationary pseudo-periodic structures in a system of gravitating particles, described by the Vlasov–Poisson system of equations. Conditions of branching of solutions of a nonlinear integral equation for a generalized gravitational potential, leading to the emergence of coherent complex states of relative equilibrium in non-stationary systems of massive particles, is studied.