Author:
Hare Kevin G,Kempton Tom,Persson Tomas,Sidorov Nikita
Abstract
Abstract
We introduce a parameter space containing all algebraic integers β ∈ (1, 2] that are not Pisot or Salem numbers, and a sequence of increasing piecewise continuous function on this parameter space which gives a lower bound for the Garsia entropy of the Bernoulli convolution ν
β
. This allows us to show that dimH(ν
β
) = 1 for all β with representations in certain open regions of the parameter space.
Funder
Natural Sciences and Engineering Research Council of Canada
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics