Chaotic dynamics in the Friedmann equation

We have studied relativistic equations and chaotic behaviors of the gravitational field on the basis of general relativity and chaotic dynamics. The Friedmann equation [the space component] shows chaotic behaviors in case of the inflation (G˙/G>0) and open (ζ = −1) universe. There occurs non-chaotic behaviors in other cases (G˙/G≦0,ζ=0,ζ=+1). We have shown the following properties of the Friedmann chaos; (1) the sensitive dependence of solutions on parameters, (2) the self-similarity of solutions in the x-x˙ plane and the x-ρ plane. Numerical calculations were carried out with the use of the microsoft EXCEL. We have also discussed the self-similarity and the hierarchy structure of the universe on the basis of E infinity theory.