On normal numbers and self-similar measures

Amir Algom; Simon Baker; Pablo Shmerkin

doi:10.1016/j.aim.2022.108276

On normal numbers and self-similar measures

Amir Algom, Simon Baker, Pablo Shmerkin

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

Abstract

Let {f_i(x)=s_i⋅x+t_i} be a self-similar IFS on R and let β>1 be a Pisot number. We prove that if [Formula presented] for some i then for every C¹ diffeomorphism g and every non-atomic self-similar measure μ, the measure gμ is supported on numbers that are normal in base β.

Original language	English
Article number	108276
Journal	Advances in Mathematics
Volume	399
DOIs	https://doi.org/10.1016/j.aim.2022.108276
State	Published - 16 Apr 2022
Externally published	Yes

Bibliographical note

Funding Information:
P.S. was supported by an NSERC discovery grant.

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

Normal numbers
Self-similar measures

ASJC Scopus subject areas

Mathematics (all)

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10.1016/j.aim.2022.108276

Cite this

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title = "On normal numbers and self-similar measures",

abstract = "Let {fi(x)=si⋅x+ti} be a self-similar IFS on R and let β>1 be a Pisot number. We prove that if [Formula presented] for some i then for every C1 diffeomorphism g and every non-atomic self-similar measure μ, the measure gμ is supported on numbers that are normal in base β.",

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AB - Let {fi(x)=si⋅x+ti} be a self-similar IFS on R and let β>1 be a Pisot number. We prove that if [Formula presented] for some i then for every C1 diffeomorphism g and every non-atomic self-similar measure μ, the measure gμ is supported on numbers that are normal in base β.

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KW - Self-similar measures

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On normal numbers and self-similar measures

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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