NONLINEAR-THEORY OF THE 2-POINT CORRELATION-FUNCTION

We consider the influence of the nonlinear stage of gravitational inst ability on the two-point correlation functions of gravitationally boun d objects. Based on the theory of nonlinear gravitational contraction of a single density peak of dissipationless matter (Gurevich and Zybin , 1988a,b; 1990) we develop a method for calculating the two-point cor relation functions of different objects of any mass. The method works good in the region of strong correlations and can be easily extended t o calculate higher correlation functions. We show that the main contri bution to the correlation function xi(i) in the region of strong corre lations xi(i) much greater than 1 is made by pair systems located outs ide large clusters of objects. In this region the shape of xi(i) is de termined only by the nonlinear dynamics of gravitational contraction o f dissipationless matter and has the form xi(i) approximate to Cr--alp ha, where alpha approximate to 1.8 is a universal parameter.