Digit frequencies and Bernoulli convolutions

作者：Kempton Tom^*

来源：Indagationes Mathematicae, 2014, 25(4): 832-842.

DOI：10.1016/j.indag.2014.04.011

• Bernoulli convolutions
• Beta-expansions
• Ergodic theory

It is well known that when beta is a Pisot number, the corresponding Bernoulli convolution v(beta) has Hausdorff dimension less than 1, i.e. that there exists a set A(beta) with v(beta)(A(beta)) = 1 and dim(H) (A(beta)) %26lt; 1. We show explicitly how to construct for each Pisot number beta such a set A beta.

• 出版日期2014-6-27