| Abstract |
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The Thue-Morse measure and its generalisations are diffraction
measures of simple aperiodic systems. Besides that, they are
paradigmatic examples of purely singular continuous probability
measures on the unit interval given as an infinite Riesz product. To
study their scaling behaviour a classical method, the thermodynamic
formalism can be used - which however has to be adapted to an
unbounded potential. Besides seeing this method, we will also see how
quantitatively the Birkhoff and dimension spectrum changes depending
on the point of the singularity. This is joint work with M. Baake, P.
Gohlke, and M. Kesseböhmer.
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