2000/02/23 by M. Piacquadio Losada, Losada, M. Piacquadio, Eda Cesaratto +2
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Theoretical and Computational Physics #math-ph #math.MP #math.PR
paper · pdf · doi:10.48550/arxiv.math-ph/0002046
35 pages, 4 figures
arxiv created 2000/02/23 · openalex publication_date 2000/02/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.