Weak Gibbs property and system of numeration

Details Weak Gibbs property and system of numeration Weak Gibbs property and system of numeration

2006-07-27

arxiv.org/abs/math/0607705v1

Mathematics

Number Theory

Scientific paper

We study the selfsimilarity and the Gibbs properties of several measures defined on the product space $\Omega\_r:=\{0,1,...,\break r-1\}^{\mathbb N}$. 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 $\beta={1+\sqrt5\over2}$, called the Erd\H os measure, and its analogue in base $-\beta=-{1+\sqrt5\over2}$, that we study by means of a suitable system of numeration.

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