Weak Gibbs property and system of numeration
Eric Olivier, Alain Thomas
Abstract
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.
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