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J. Analyse Math., 2020, Volume 141, Issue 1, Pages 165–205 (Mi janm2)  

A spectral cocycle for substitution systems and translation flows

A. I. Bufetovabc, B. M. Solomyakd

a Aix-Marseille Université
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
d Bar-Ilan University, Department of Mathematics

Abstract: For substitution systems and translation flows, a new cocycle, which we call the 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.

DOI: https://doi.org/10.1007/s11854-020-0127-2


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