Abstract
Nonlinear oscillations in the dynamic system of gravitational and material fields are considered. The problems of singularities and caustics in gravity, expansion and baryon asymmetry of the Universe, wave prohibition of collapse into black holes, and failure of the Big Bang concept are discussed. It is assumed that the effects of the expansion of the Universe are coupling with the reverse collapse of dark matter. This hypothesis is used to substantiate the vortex and fractal structures in the distribution of matter. A system of equations is proposed for describing turbulent and fluctuation processes in gravitational and material fields. Estimates of the di usion parameters of such a system are made in comparison with the gravitational constant.