Non-linear scale invariance in a cold dark matter universe

The observed decomposition of the lowest (N = 3.4) N-point correlation functions in symmetrized (N - 1) products of two-point correlation functions suggest the possibility that the Universe may obey a specific scale invariance, at least in some range. We investigate the possibility that the non-linear evolution in a CDM Universe indeed leads to such a scale invariance. We determine the count probabilities in a galaxy catalog generated with a P3M simulation code by Davis and Efstathiou. We then proceed to check some of the expected scaling model predictions concerning the volume size and the count number dependence. Our results are consistent with the the scale invariance predictions. We also compute some fractal properties of the sample. The distribution appears to be essentially a bifractal