Tanja Schindler

Multifractal analysis of the Thue--Morse measure

For bounded potentials the thermodynamic formalism has long been studied and gives a possibility to obtain the Birkhoff and the dimension spectrum for a Hölder continuous potential. However, in order to execute a multifractal analysis for the Thue-Morse measure one needs to consider an unbounded potential. The Thue--Morse measure is a paradigmatic example of a purely singular continuous probability measure on the unit interval given as an infinite Riesz product and has its origin in aperiod dynamics. Using some adjustments to the classical method of the thermodynamic formalism we will determine the Birkhoff and the dimension spectrum of the Thue-Morse measure.
This is joint work with M. Baake, P. Gohlke, and M. Kesseböhmer.