The thermodynamic formalism for bounded potentials has longbeen studied. However, in order to execute a multifractal analysis forthe Thue-Morse measure (a paradigmatic example of a purely singular continuous probability measure on the unit interval given as an infinite Riesz product), one needs to consider an unbounded potential. Using some adjustments to the classical method of the thermodynamical for-malism, I 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
