On singular substitution Z-actions

Abstract: We consider primitive aperiodic substitutions on $d$ letters and the spectral properties of associated dynamical systems. In an earlier work we introduced a spectral cocycle, related to a kind of matrix Riesz product, which extends the (transpose) substitution matrix to the $d$-dimensional torus. The asymptotic properties of this cocycle provide local information on the (fractal) dimension of spectral measures. In the talk I will discuss a sufficient condition for the singularity of the spectrum in terms of the top Lyapunov exponent of this cocycle.

This is a joint work with A. Bufetov.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper )

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One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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