Abstract
According to astrophysical observations value of recession velocity in a certain point is proportional to a distance to this point. The proportionality coefficient is the Hubble constant measured with 5% accuracy In this article, the gravitational wave equation was obtained in the form of the oscillation equation from the Einstein theory depending on the coordinates. The numerical results analysis of the system of equations is obtained. For different values of the Hubble parameter, the phase portrait of the dynamical system was taken and the dimensions of the attractors were determined. The expansion of the universe is characterized by the maximum value of the scaling index; these numerical values were taken theoretically in our earlier works.