Spectral cocycle for substitution systems and translation flows

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

Catégories Pas de Catégories

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.


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