On the Gibbs properties of Bernoulli convolutions related to \(\beta\)-numeration in multinacci bases
type: Item
instance of: scholarly article
title: On the Gibbs properties of Bernoulli convolutions related to \(\beta\)-numeration in multinacci bases
zbMATH Open document ID: 1076.28002
author: Eric Olivier
author: Nikita Sidorov
author: Alain Thomas
published in: Monatshefte für Mathematik
publication date: 2005-08-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0411278
full work available at URL: on-the-gibbs-properties-of-bernoulli-convolutions-related-to-numeration-in-multinacci-bases(6cc12d48-d957-424f-9f45-0d1e2c21e779).html
review text: 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.
reviewed by: Thomas B. Ward
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 11A67
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 37A45
Mathematics Subject Classification ID: 37C45
zbMATH DE Number: 2193072
zbMATH Keywords: weak Gibbs measure
zbMATH Keywords: Bernoulli convolution
zbMATH Keywords: PV-number
zbMATH Keywords: continued fraction
MaRDI profile type: Publication
OpenAlex ID: W2060219434
arXiv ID: math/0411278
DOI: 10.1007/S00605-005-0298-Z
description: scientific article