2010/06/18 by Éric Olivier, Olivier, Éric, Alain Thomas +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Dynamics and Fractals #Theoretical and Computational Physics #math.DS #math.GM
paper · pdf · doi:10.48550/arxiv.1006.3616
We have included the content of this paper in arXiv:0908.4171
openalex publication_date 2010/06/18 · arxiv created 2014/12/30 · arxiv updated 2014/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we give an example of uniform convergence of the sequence of column vectors A1… AnV\over\Vert A1… AnV\Vert, Ai∈\A,B,C\, A,B,C being some (0,1)-matrices of order 7 with much null entries, and V a fixed positive column vector. These matrices come from the study of the Bernoulli convolution in the base β>1 such that β3=2β2-β+1, that is, the (continuous singular) probability distribution of the random variable (β-1)∑n=1^∞ωn\overβn when the independent random variables ωn take the values 0 and 1 with probability 1\over2. In the last section we deduce, from the uniform convergence of A1… AnV\over\Vert A1… AnV\Vert, the Gibbs and the multifractal properties of this measure.