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Mathematics > Dynamical Systems
Title: On normal numbers and self-similar measures
(Submitted on 6 Jul 2021 (v1), revised 15 Jul 2021 (this version, v2), latest version 22 Nov 2021 (v3))
Abstract: In this paper we prove that if $\{\varphi_i(x)=\lambda x+t_i\}$ is an equicontractive iterated function system and $b$ is a positive integer satisfying $\frac{\log b}{\log |\lambda|}\notin\mathbb{Q},$ then almost every $x$ is normal in base $b$ for any non-atomic self-similar measure of $\{\varphi_i\}$.
Submission history
From: Simon Baker [view email][v1] Tue, 6 Jul 2021 16:01:52 GMT (12kb)
[v2] Thu, 15 Jul 2021 08:12:19 GMT (13kb)
[v3] Mon, 22 Nov 2021 14:34:48 GMT (13kb)
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