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arXiv · 1802.04783

A spectral cocycle for substitution systems and translation flows

Alexander I. Bufetov·Boris Solomyak
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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.

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Alexander I. Bufetov, Boris Solomyak. 2018-02-13. A spectral cocycle for substitution systems and translation flows. https://arxiv.org/abs/1802.04783

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