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Multifractal Spectrum and Thermodynamical Formalism of the Farey Tree

M. Piacquadio Losada·E. Cesaratto
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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.

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M. Piacquadio Losada, E. Cesaratto. 2000-02-23. Multifractal Spectrum and Thermodynamical Formalism of the Farey Tree. https://arxiv.org/abs/math-ph/0002046

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