On the Gibbs properties of Bernoulli convolutions related to \(\beta\)-numeration in multinacci bases
Bernoulli convolutions have a long history -- they were extensively studied by \textit{P. Erdős} in 1939 [Am. J. Math. 61, 974--976 (1939; Zbl 0022.35402)] for example -- and have found application in several areas, including fractal geometry and ergodic theory. Here the Bernoulli convolutions associated to \(\beta\)-numeration systems are studied, and in the case where \(\beta\) is a Pisot--Vijayaraghavan number a matrix decomposition is found. For the case of ``multinacci'' \(\beta\) a multifractal analysis of the measures is possible.
scientific article