Digit Frequencies and Bernoulli Convolutions

Tom Kempton

doi:10.1016/j.indag.2014.04.011

Digit Frequencies and Bernoulli Convolutions

Tom Kempton^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

It is well known that when ββ is a Pisot number, the corresponding Bernoulli convolution νβνβ has Hausdorff dimension less than 11, i.e. that there exists a set AβAβ with νβ(Aβ)=1νβ(Aβ)=1 and dimH(Aβ)<1dimH(Aβ)<1. We show explicitly how to construct for each Pisot number ββ such a set AβAβ.

Original language	English
Pages (from-to)	832-842
Number of pages	11
Journal	Indagationes Mathematicae
Volume	25
Issue number	4
DOIs	https://doi.org/10.1016/j.indag.2014.04.011
Publication status	Published - 27 Jun 2014

Keywords

Bernoulli convolutions
Beta-expansions
Ergodic theory

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10.1016/j.indag.2014.04.011

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title = "Digit Frequencies and Bernoulli Convolutions",

abstract = "It is well known that when ββ is a Pisot number, the corresponding Bernoulli convolution νβνβ has Hausdorff dimension less than 11, i.e. that there exists a set AβAβ with νβ(Aβ)=1νβ(Aβ)=1 and dimH(Aβ)<1dimH(Aβ)<1. We show explicitly how to construct for each Pisot number ββ such a set AβAβ.",

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AB - It is well known that when ββ is a Pisot number, the corresponding Bernoulli convolution νβνβ has Hausdorff dimension less than 11, i.e. that there exists a set AβAβ with νβ(Aβ)=1νβ(Aβ)=1 and dimH(Aβ)<1dimH(Aβ)<1. We show explicitly how to construct for each Pisot number ββ such a set AβAβ.

KW - Bernoulli convolutions

KW - Beta-expansions

KW - Ergodic theory

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DO - 10.1016/j.indag.2014.04.011

M3 - Article

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JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 4

ER -

Digit Frequencies and Bernoulli Convolutions

Abstract

Keywords

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