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Scaling properties of the Thue–Morse measure

Baake, Michael; Gohlke, Philipp; Kesseböhmer, Marc; Schindler, Tanja


The classic Thue–Morse measure is a paradigmatic example of a purely singular continuous probability measure on the unit interval. Since it has a representation as an infinite Riesz product, many aspects of this measure have been studied in the past, including various scaling properties and a partly heuristic multifractal analysis. Some of the difficulties emerge from the appearance of an unbounded potential in the thermodynamic formalism. It is the purpose of this article to review and...[Show more]

CollectionsANU Research Publications
Date published: 2019
Type: Journal article
Source: Discrete and Continuous Dynamical Systems, Series A
DOI: 10.3934/dcds.2019168
Access Rights: Open Access


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