Weak Gibbs property and system of numeration

2006/07/27 by Éric Olivier, Eric Olivier, Olivier, Eric +2
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #11A55 #11A63 #11A67 #28A12 #Complex Systems and Time Series Analysis #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Statistical Mechanics and Entropy #math.NT #msc:11A55 #msc:11A63 #msc:11A67 #msc:28A12

paper · pdf · doi:10.48550/arxiv.math/0607705

arxiv created 2006/07/27 · openalex publication_date 2006/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the selfsimilarity and the Gibbs properties of several measures defined on the product space Ω_r:=\0,1,...,\break r-1\^{\mathbb N}. This space can be identified with the interval [0,1] by means of the numeration in base r. The last section is devoted to the Bernoulli convolution in base β=1+√5\over2, called the Erd\H os measure, and its analogue in base -β=-1+√5\over2, that we study by means of a suitable system of numeration.

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