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

Mathematics

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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 C ¹ 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
Number of pages	17
Journal	Advances in Mathematics
Volume	399
Early online date	22 Feb 2022
DOIs	https://doi.org/10.1016/j.aim.2022.108276
Publication status	Published - 16 Apr 2022

Keywords

Normal numbers
Self-similar measures

ASJC Scopus subject areas

Mathematics(all)

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Cite this

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AU - Baker, Simon

AU - Shmerkin, Pablo

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KW - Self-similar measures

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On normal numbers and self-similar measures

Abstract

Keywords

ASJC Scopus subject areas

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