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.
Original language | English |
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Article number | 108276 |
Journal | Advances in Mathematics |
Volume | 399 |
DOIs | |
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)