A spectral cocycle for substitution systems and translation flows

Abstract

For substitution systems and translation flows, a new cocycle, which we call {\em spectral cocycle}, is introduced, whose Lyapunov exponents govern the local dimension of the spectral measure for higher-level cylindrical functions. The construction relies on the symbolic representation of translation flows and the formalism of matrix Riesz products.

Corrected a few typos. To appear in Journal d'Analyse Mathematique