The Hentschel-Procaccia Conjecture

Details The Hentschel-Procaccia Conjecture The Hentschel-Procaccia Conjecture

2000-01-13

arxiv.org/abs/cond-mat/0001197v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

Extensive confusion exists and persists in the literature on dynamical systems theory, cosmology, and other fields over spectra of fractal dimensions. Entirely different generating functions have been treated as if they should yield identical spectra, or scaling exponents. An uncritical implicit assumption of universality of scaling exponents is made, even though there is no good theoretical reason to expect scaling exponents to be universal away from criticality. Expectations based on the unphysical and empirically inapplicable zero length scale limit (which would require infinite precision in data analysis) are often taken for granted. A source of confusing together different generating functions can be traced back to the Hentschel-Procaccia conjecture, which I prove to be wrong for the case of data analysis in the only applicable limit, that of finite precision. The two different definitions of 'multifractal' stated by Mandelbrot and by Halsey et are compared and contrasted.

Affiliated with

Also associated with

No associations

Rating

The Hentschel-Procaccia Conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Hentschel-Procaccia Conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Hentschel-Procaccia Conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-360675