Weak Gibbs property and system of numeration

الأصل · EN

We study the selfsimilarity and the Gibbs properties of several measures defined on the product space Ω_r:={0,1,..., r-1}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+√52, called the Erd os measure, and its analogue in base -β=-1+√52, that we study by means of a suitable system of numeration.