Dynamical Systems seminar - The Thue-Morse measure: multifractal analysis and superpolynomial scaling

Dates

Wednesday, October 6, 2021 - 14:00 to 15:00

Speaker: Philipp Gohlke (Bielefeld University)

The Thue-Morse measure is a paradigmatic example of a singular continuous measure that arises from a system of aperiodic order. Its properties have been studied extensively in the past, including a partly heuristic multifractal analysis in the mathematical physics literature.

The aim of a multifractal analysis is to obtain a detailed understanding of the scaling behaviour of the measure around individual points. We revisit this analysis in the framework of the thermodynamic formalism, interpreting the Thue-Morse measure as an equilibrium measure for a potential with a singularity. This singularity gives rise to a superpolynomial scaling behaviour around dyadic points and produces a pathological feature in the multifractal spectrum.