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Seminarium i matematik

A multifractal analysis of a singular potential and its equilibrium measure

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Potentials with logarithmic singularities occur naturally in the study of dynamical systems, for example, in systems with a zero of the derivative. They also appear in some number theoretical problems or in the study of substitution dynamical systems.  We consider Thue-Morse (TM) measure which we regard as the (unique) equilibrium measure of a potential with logarithmic singularity.  We study the uncommon fast scaling of the Birkhoff sums of the potential and the TM-measure by conducting multifractal analysis, using tools from thermodynamic formalism, which however has to be adapted to an unbounded potential. This is joint work with Ph. Gohlke and J. Schmeling.

B1006 Georgios Lamprinakis, Lunds universitet Lägg till i din kalender