# Spectral cocycle for substitution systems and translation flows – Boris Solomyak

Boris Solomyak
University of Bar-Ilan, Israel
https://u.math.biu.ac.il/~solomyb/personal.html

Date(s) : 05/10/2018   iCal
9 h 30 min - 10 h 30 min

To a primitive substitution system, we assign a complex matrix cocycle, defined over a toral endomorphism induced by the substitution matrix. It is closely related to the spectral theory of suspension flows over the substitution system; in particular, the local dimension of spectral measures is expressed in terms of the top Lyapunov exponent of the cocycle. As an application, we obtain a sufficient condition for the singularity of a typical flow.

The construction and the results are also extended to S-adic system and translation flows.
Based on joint work with A. Bufetov. https://hal.archives-ouvertes.fr/hal-02110664

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