Spectral cocycle for substitution systems and translation flows
Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03
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.