Multifractal Spectrum and Thermodynamical Formalism of the Farey Tree
Mathematical Physics
2007-05-23 v1 math.MP
Probability
Abstract
The task of comparing the Hausdorff spectrum, the computational spectrum, and the Legendre spectrum of a fractal set endowed with a probability measure, was tackled by several authors - Cawley and Mauldin, Riedi and Mandelbrot, among others. For self-similar measures all three spectra coincide. We compare these spectra for the hyperbolic measure (inducing the Farey Tree partition), fundamentally different from the self-similar one.
Keywords
Cite
@article{arxiv.math-ph/0002046,
title = {Multifractal Spectrum and Thermodynamical Formalism of the Farey Tree},
author = {M. Piacquadio Losada and E. Cesaratto},
journal= {arXiv preprint arXiv:math-ph/0002046},
year = {2007}
}
Comments
35 pages, 4 figures