Are galaxy distributions scale invariant ? A perspective from dynamical systems theory

@inproceedings{McCauley1997AreGD,
title={Are galaxy distributions scale invariant ? A perspective from dynamical systems theory},
author={Joseph L. McCauley},
year={1997}
}

Unless there is evidence for fractal scaling with a single exponent over distances .1 ≤ r ≤ 100hMpc then the widely accepted notion of scale invariance of the correlation integral for .1 ≤ r ≤ 10hMpc must be questioned. The attempt to extract a scaling exponent ν from the correlation integral n(r) by plotting log(n(r)) vs. log(r) is unreliable unless the underlying point set is approximately monofractal. The extraction of a spectrum of generalized dimensions νq from a plot of the correlation… CONTINUE READING